E-prints can be downloaded from the arxiv.org and its mirror sistes.

Slide of invited talk at the 31st Symposium of History of Mathematics (October 16-17, 2021, Tsudajuku University, On-line) [pdf file]

Kanehisa Takasaki

Phys. A: Math. Theor. (to appear), https://doi.org/10.1088/1751-8121/ac1828

J. Phys. A: Math. Theor. 54 (2021), 35LT02

doi: 10.1088/1751-8121/ac1828

arXiv:2103.10666

Comments: latex2e using packages amsmath,amssymb,amsthm; (v2) A typo in the definition of E_k(z) on page 6 corrected

MSC-class: 14N35, 37K10

Kanehisa Takasaki

Slide file of invited talk at on-line workshop "Quantum Geometry in Gauge Theory and Strings" (November 21, 2020) [pdf file]

Kanehisa Takasaki

Abstract of talk at MSJ annual meeting (Nihon University, March 16--19, 2020) cancelled because of the COVID-19 epidemic [pdf file (partly corrected)]

Kanehisa Takasaki

RIMS Kokyuroku Bessatsu B87 (2021), 057–078.

arXiv:2002.00660

Comments: latex2e, 21pages, no figure, submitted to proceedings of RIMS workshop "Mathematical structures of integrable systems, its deepening and expansion" (September 9-11, 2019)

MSC-class: 05E10, 14N10, 37K10

Kanehisa Takasaki

Proceedings of Symposia in Pure Mathematics, vol. 103.1, Amer. Math. Soc., Providence, RI, 2021, pp. 481-502

arXiv:1909.13095

Comments: latex2e, amsmath,amssymb,amsthm, 29pp, no figure, contribution to Boris Dubrovin memorial volume, American Mathematical Society

Kanehisa Takasaki

Invited talk at RIMS workshop ``Mathematical structures of integrable systems, its deepening and expansion'' (September 9-11, 2019) [slide]

Kanehisa Takasaki

Invited talk at China-Japan Joint Workshop on Integrable Systems 2019 (Shonan Village Center, Hayama, Japan, August 18-23, 2019) [slide]

Toshio Nakatsu and Kanehisa Takasaki

Comm. Math. Phys. 376(1) (2020), 201-234

https://doi.org/10.1007/s00220-019-03648-5

arXiv:1812.11726

Comments: 44 pages, 2 figures

Kanehisa Takasaki

Invited talk at SIDE13 conference (Hakata, japan, November 13, 2018) [slide]

2. Deriving q-Toda equations from Toda hierarchy

3. Toda-like equations for U(1) Nekrasov functions

4. Dual partition function of 5D SU(N) theory

5. Conclusion

Kanehisa Takasaki

(previous title: Quantum curve and 4D limit of melting crystal model)

Journal of Geometry and Physics 137C (2019), 184--203

DOI: 10.1016/j.geomphys.2018.12.012

arXiv:1704.02750 [math-ph]

Date (revised v2): Tue, 28 Aug 2018 21:26:40 GMT (21kb)

Comments: latex2e using packages amsmath,amssymb,amsthm, 35 pages, no figure; (v2) the title is changed, and an appendix on the relevance to the Toda hierarchy is added; (v3) texts in Introduction and Sect. 4.2 are modified, a few typos are corrected, final version for publication

MSC-class: 14N35, 37K10, 39A13

Kanehisa Takasaki

invited talk at Special session 49, AIMS Conferencer 2018 (Taipei, Taiwan, July 7, 2018) [slide]

2. Lax equations in single Hurwitz sector

3. Perspective from generalized string equations

Kanehisa Takasaki

J. Phys. A: Math. Theor. 51 (2018), 43LT01 (9 pages)

doi: 10.1088/1751-8121/aae10b

arXiv:1807.00085

Comments: latex2e, amsmath,amssymb,amsthm, 12 pages, no figure

MSC-class: 14N10, 37K10

Kanehisa Takasaki

invited talk at IBS Center of Geometry and Physics, Pohang, Korea (March 27, 2018) [slide]

Kanehisa Takasaki

J. Phys. A: Math. Theor. 51 (2018), 203001 (35pp)

doi: 10.1088/1751-8121/aabc14

arXiv:1801.09924 [math-ph]

Comments: 46 pages, no figure, contribution to JPhysA Special Issue "Fifty years of the Toda lattice"

MSC classes: 17B65, 37K10, 82B20

Kanehisa Takasaki

invited talk at Conference ``Physics and Mathematics of Nonlinear Phenomena'' (Gallipoli, Italy, June 17-24, 2017) [slide]

Kanehisa Takasaki and Toshio Nakatsu

Talk at the autumn meeting of the Mathematical Society of Japan (Kansai University, September 15--18, 2016) [slide]

Kanehisa Takasaki and Toshio Nakatsu

SIGMA 13 (2017), 009, 28 pages

doi:10.3842/SIGMA.2017.009

arXiv:1609.00882 [math-ph]

Comments: Contribution to the Special Issue on Combinatorics of Moduli Spaces: Integrability, Cohomology, Quantisation, and Beyond

MSC-class: 37K10, 39A13, 81T30

Key words: topological vertex; mirror symmetry; quantum curve; q-difference equation; KP hierarchy; Kac-Schwarz operator

Kanehisa Takasaki

Invited Talk at Workshop on Applied Analysis (Osaka, May 19-21, 2016) [slide]

Gekhtman, Shapiro and Veinstein constructed Toda-type integrable systems on the double Bruhat cells $G^{u,v} \subset G = \mathrm{GL}(n,\CC)$ of Coxeter elements $u,v$ of $S_n$. This is an application of Berenstein, Fomin and Zelevinsky's matrix factorization, and presents a generalization of Feybusovich and Gekhtman's ``elementary Toda orbits''. I review elementary part of this topic.

Kanehisa Takasaki

Invited talk at international symposium ``Rikkyo MathPhys 2016'' (Rikkyo University, January 9--11, 2016) [slide]

Kanehisa Takasaki

Invited talk at workshop ``Quantization of Spectral Curves'' (Osaka City University, November 2--6, 2015) [slide]

Kanehisa Takasaki and Toshio Nakatsu

Talk at the autumn meeting of the Mathematical Society of Japan (Kyoto Sangyo University, September 13--16, 2015) [slide]

Kanehisa Takasaki and Toshio Nakatsu

J. Phys. A: Math. Theor. 49 (2016), 025201 (28pp)

doi:10.1088/1751-8113/49/2/025201

arXiv:1507.07053 [math-ph]

Comments: latex2e, package amsmath,amssymb,amsthm,graphicx, 10 figures

MSC-class: 17B81, 33E20, 81T30

Kanehisa Takasaki

Invited talk at workshop ``Recent Progress of Integrable Systems'', National Taiwan University, April 10-12, 2015 [slide]

This is an expanded version of my talk at Tsuda College, Tokyo, in February, 2015.

Kanehisa Takasaki

Invited talk at workshop ``Curves, Moduli and Integrable Systems'', Tsuda College, Tokyo, February 17-19, 2015 [slide]

Kanehisa Takasaki

Invited talks in the 16th "Singularity Workshop" (Nagoya University, January 10-12, 2015) [slides]

1. Levi-Civita connection in terms of moving frames

2. Spinor bundles and spinor connecions

3. Anti-selfdual spacetimes

II. Construction and inverse-construction of twistor spaces

1. Twistor space of anti-selfdual spacetime

2. Twistor space of right-flat spacetime

3. Generation of right-flat spacetime

4. Example of generation

III. Dimensional reductions and integrable systems

1. Example of dimensional reduction: dispersionless Toda equation

2. Example of dimensional reduction: dispersionless KP equation

3. Three-dimensional Einstein-Weyl spaces

Kanehisa Takasaki

J. Phys. A: Math. Theor. 48 (2015), 215201 (34 pages)

doi:10.1088/1751-8113/48/21/215201

arXiv:1410.5060 [math-ph]

Comments: 41 pages, no figure

MSC-class: 17B65, 35Q55, 81T30, 82B20

Kanehisa Takasaki

Invited talk at workshop "Various aspects of nonlinear mathematical models: continuous, discrete, ultra-discrete, and beyond" (IMI, Kyushu University, August 6-8, 2014) [slide | report]

Kanehisa Takasaki

Talk at MSJ annual meeeting (Gakushuin University, March 13, 2014) [abstract | slide]

Kanehisa Takasaki

J. Phys.: Conf. Ser. 482 (2014), 012041 [open access]

doi:10.1088/1742-6596/482/1/012041

arXiv:1312.7276 [math-ph]

Comments: 10 pages, 4 figures, contribution to proceedings of the conference "Physics and Mathematic of Nonlinear Phenomena", Gallipoli, Italy, June 23-28, 2013

MSC-class: 17B65, 35Q55, 81T30, 82B20

Kanehisa Takasaki

J. Phys. A: Math. Theor. 47 (2014), 165201 (20 pages)

doi:10.1088/1751-8113/47/16/165201

arXiv:1312.7184 [math-ph]

Comments: 24pages, 1 figre

MSC-class: 17B80, 35Q55, 81T30

Kanehisa Takasaki

Invited talk at "Physics and Mathematic of Nonlinear Phenomena", Gallipoli, Italy, June 23--28, 2013 [slide]

Contents:

1.Melting crystal model --- 3D Young diagram, plane partitions, partition function, diagonal slicing, partial sums, final answer

2.Integrable structure in deformed models --- undeformed models, deformation by external potentials, summary of previous result, summary of new result

3. Fermionic approach to partition functions --- fermions, fermionic representation of partition functions, previous result, new result, technical clue

4. Integrable structure in Lax formalism --- Lax formalism of 2D Toda hierarchy, reduction to 1D Toda hierarchy, reduction to Ablowitz-Ladik hierarchy, result, technical clue

Kanehisa Takasaki

talk presented at the Annual Meeting of the Mathematical Society of Japan (Kyoto University, March 22, 2013) [abstract| slide]

Kanehisa Takasaki

J. Phys. A: Math. Theor. 46 (2013), 245202 (23 pages)

arXiv:1302.6129 [math-ph]

Comments: latex2e, 33 pages, no figure

MSC classes: 17B65, 35Q55, 81T30, 82B20

doi:10.1088/1751-8113/46/24/245202

Kanehisa Takasaki

RIMS Kokyuroku No. 1913 (2014), 182--201

arXiv:1301.4548 [math-ph]

Comments: 20 pages, 3 figures, contribution to the proceedings of the RIMS camp-style seminar "Algebraic combinatorics related to Young diagrams and statistical physics", August, 2012, International Institute for Advanced Studies, Kyoto, organized by M. Ishikawa, S. Okada and H. Tagawa

MSC-class: 05E05, 37K10, 81T30

Kanehisa Takasaki

Poster presentation at conference "Integrability in Gauge and String Theory", ETH Zurich, August 20--24, 2012 [poster]

arXiv version arXiv:1208.4497 [math-ph]]

MSC-class: 17B65, 35Q58, 82B20

Kanehisa Takasaki

Invited talk at RIMS camp-style seminar "Algebraic Combinatorics Related to Young Diagrams and Statistical Physics", IIAS, Kyoto, August 6 - 10, 2012 [slide]

1. Topological vertex and web diagrams

2. Generalized conifolds

3. Partition functions of generalized conifolds

4. Simplest examples

5. General rules

6. Quantum mirror curve

Kanehisa Takasaki

SIGMA 8 (2012), 102, 22 pages

arXiv:1206.1151 [math-ph]

Contribution to SIGMA Special Issue on Geometrical Methods in Mathematical Physics

DOI: 10.3842/SIGMA.2012.102

MSC classes: 35Q58, 37K10, 53B50, 53D45

A. Yu. Orlov, T. Shiota, K. Takasaki

arXiv:1201.4518v1 [math-ph]

Kanehisa Takasaki and Takashi Takebe

Analysis and Mathematical Physics 2 (2012), 171-214.

arXiv:1112.0601v1 [math-ph]

Comments: 37 pages, no figures. arXiv admin note: substantial text overlap with arXiv:0912.4867

MSC classes: 37K10, 35Q53

Kanehisa Takasaki and Toshio Nakatsu

J. Phys. A: Math. Theor. 45 (2012), 025403 (38pp)

arXiv:1110.0657 [math-ph]

Comments: latex2e, 55 pages, no figure

MSC-class: 35Q58, 81T13, 82B20

doi:10.1088/1751-8113/45/2/025403

Kanehisa Takasaki

Invited talk at "7th International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory" (University of Georgia, Athens, April 5, 2011) [slide]

I will also argue that a possible dispersive analogue of these results can be found in a system of multiple bi-orthogonal polynomials. These multiple bi-orthogonal polynomials are a generalizations of bi-orthogonal polynomials studied by Adler and van~Moerbeke in the context of the Toda hierarchy. The latter give a special solution of the Toda hierarchy. This solution may be thought of as a dispersive counterpart of non-degenerate solution of the dispersionless Toda hierarchy. I conjecture that a similar interpretation holds for the multiple bi-orthogonal polynomials in the framework of our previous work.

Kanehisa Takasaki

colloquium talk at Department of Mathematics, University of California, Davis (Davis, March 30, 2011) [slide]

Kanehisa Takasaki and Takashi Takebe

Theoretical and Mathematical Physics 171 (2) (2012), 683-690.

arXiv:1105.0794v1 [math-ph]

Comments: 12 pages, contribution to the Proceedings of the "International Workshop on Classical and Quantum Integrable Systems 2011" (January 24-27, 2011 Protvino, Russia)

Kanehisa Takasaki

Acta Polytechnica 51, No.1 (2011), 74-76.

arXiv:1101.4083 [math-ph]

Comments: latex2e using packages amsmath,amssymb,amsthm, 6 pages, no figure, contribution to "19th International Colloquium on Integrable Systems and Quantum Symmetries"

Kanehisa Takasaki

arXiv:1012.5554 [math-ph]

Journal of Geometry and Physics 62 (2012), 1135--1156

Comments: latex2e using amsmath,amssymb,amsthm, 41 pages, no figure

MSC-class: 35Q58, 14N10, 81R12

Kanehisa Takasaki

(Workshop ``Integrable Systems, Random Matrices, Algebraic Geometry and Geometric Invariants'', Kyoto University, December 15-17, 2010) [slides of talk]

K. Takasaki

(MSJ Autumn Meeting, Nagoya University, September 22-25, 2010) [slides of talk]

K. Takasaki

19th International Colloquium ``Integrable Systems and Quantum Symmetries'' (Czech Technical University, Prague, June 17--19, 2010) slides of talk [pdf]

Kanehisa Takasaki, Takashi Takebe and Lee Peng Teo

J. Phys. A: Math. Theor. 43 (2010), 325205

arXiv:1003.5767 [math-ph]

Comments: latex2e, using amsmath, amssym and amsthm packages, 32 pages, no figure

Kanehisa Takasaki

(MSJ spring meeting, University of Keio, March 24--27, 2010) [abstract of talk | slides of talk]

Kanehisa Takasaki

B. Feigin, M. Jimbo and M. Okado (eds.), ``New Trends in Quantum Integrable Systems'', Proceedings of the Infinite Analysis 09, Kyoto, Japan 27-31 July 2009 (World Sci. Publ., Hackensack, NJ), pp. 373--391.

arXiv:1003.307 [math-ph]

Comments: latex2e, using ws-procs9x6 package, 19 pages, contribution to the festschrift volume for the 60th anniversary of Tetsuji Miwa

Kanehisa Takasaki

J. Phys. A: Math. Theor. 43 (2010) 434032

arXiv:1002.4688 [nlin.SI]

Comments: latex2e, usepackage amsmath,amssymb, 19 pages, no figure

Kanehisa Takasaki and Takashi Takebe

arXiv:0912.4867 [math-ph]

Comments: 28 pages

Kanehisa Takasaki

Slides of talk at RIAM workshop ``Currrent and Future Research on Nonlinear Waves'' (RIAM, Kyushu University, October 19--21, 2009) [pdf]

Kanehisa Takasaki

Slides of talk at MSJ autumn meeting (Osaka University, September 24--27, 2009) [pdf]

Kanehisa Takasaki

SIGMA 5 (2009), paper 109, 34 pages

arXiv:0908.3569 [nlin.SI]

Comments: 49 pages, no figure, usepackage amsmath,amssymb,amsthm

Kanehisa Takasaki

Workshop ``Infinite Analysis 09 --- New trends in quantum integrable systems'' (RIMS and Department of Mathematics, Kyoto University, July 27--31, 2009), slides of talk [pdf]

Kanehisa Takasaki

slides of talk at MSJ spring meeting 2009 (Graduate School of Mathematical Science, University of Tokyo, March 26--29, 2009) [pdf]

Kanehisa Takasaki

slides of talk at MSJ spring meeting 2009 (Graduate School of Mathematical Science, University of Tokyo, March 26--29, 2009) [pdf]

Kanehisa Takasaki

arXiv:0903.2607 [math-ph]

J. Geometry and Physics 59 (2009), 1244-1257

Comments: 27 pages, no figure, latex2e(package amsmath,amssymb,amsthm)

Kanehisa Takasaki

slides of talk at workshop ``Laplacian Growth and Related Topics'' (CRM, University of Montreal, August 18--22, 2008) [pdf]

Kanehisa Takasaki and Takashi Takebe

J. Phys. A: Math. Theor. {\bf 41} (2008), 475206 (27pp)

arXiv:0808.1444 [nlin.SI]

Comments: latex 2e, 39 pages, using packages amsmath,amssymb,amsthm

Toshio Nakatsu and Kanehisa Takasaki

Advanced Studies in Pure Mathematics, vol. 59 (Mathematical Society of Japan, 2010), pp. 201--223.

arXiv:0807.4970 [math-ph]

Comments: 21 pages, 3 figures, using amsmath,amssymb,amsthm,graphicx packages, contribution to proceedings of RIMS workshop "New developments in Algebraic Geometry, Integrable Systems and Mirror symmetry" (January 7--11, 2008)

Toshio Nakatsu, Yui Noma and Kanehisa Takasaki

arXiv:0807.0746 [hep-th]

Nucl. Phys. B808 (2009), 411--440

Comments: The solution of the Reimann-Hilbert problem presented here is wrong. A correct solution, along with a correct curve, can be obtained by solving a Riemann-Hilbert problem for the primitive function of the Phi potential.

Toshio Nakatsu, Yui Noma and Kanehisa Takasaki

arXiv:0806.3675 [hep-th]

Int. J. Mod. Phys. A23 (2008), 2332-2342.

Comments: The solution of the Reimann-Hilbert problem presented here is wrong. A correct solution, along with a correct curve, can be obtained by solving a Riemann-Hilbert problem for the primitive function of the Phi potential.

12 pages, 1 figure, based on an invited talk presented at the international workshop "Progress of String Theory and Quantum Field Theory" (Osaka City University, December 7-10, 2007), to be published in the proceedings

Kanehisa Takasaki

slides of talk at workshop "New developments in Algebraic Geometry, Integrable Systems and Mirror symmetry" (RIMS, January 7 - 11, 2008) [pdf]

Kanehisa Takasaki

Advanced Studies in Pure Mathematics vol. 61 (Mathematical Society of Japan, 2011), pp. 387--441.

arXiv:0710.5356 [nlin.SI]

Comments: latex2e, packages "amsmath,amssymb,amsthm", 50 pages, no figure, contribution to proceedings of conference "Exploration of new structures and natural constructions in mathematical physics" (Nagoya University, March, 2007); (v2) a few references added; (v3) final version for publication

Toshio Nakatsu and Kanehisa Takasaki

arXiv:0710.5339 [hep-th]

Commun. Math. Phys. 285 (2009), 445--468

Comments: 30 pages, 4 figures

Kanehisa Takasaki

slides of talk at Workshop ``Exploration of New Structures and Natural Construction in Mathematical Physics'' (Nagoya University, March 5--8, 2007) [pdf]

Kanehisa Takasaki

Contribution to proceedings of RIMS workshop ``Prospects of theories of integrable systems'' (August 21--23, 2006) [pdf]

Kanehisa Takasaki

arXiv:nlin.SI/0610073

SIGMA 3 (2007), 042, 32 pages

Contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics

Kanehisa Takasaki and Takashi Takebe

slides of talk at MISGRAM workshop "Integrable Systems in Applied Mathematics", Madrid, September 7--12, 2006 [pdf]

Kanehisa Takasaki and Takashi Takebe

arXiv:nlin.SI/0608068

Physica D235, no. 1-2 (2007), 109-125

Comments: latex2e (a4paper, 12pt) using packages "amssymb,amsmath,amsthm", 44 pages, no figure

Kanehisa Takasaki

contribution to proceedings of RIMS workshop ``Hyperfunctions and Linear Differential Equations 2006'' (March 6--9, 2006) [pdf]

Kanehisa Takasaki

SIGMA Vol. 2 (2006), Paper 057, 22 pages

Comments: 31 pages, no figure, latex2e usepackage amsmath,amssymb

Report-no: nlin.SI/0604003

Kanehisa Takasaki and Takashi Takebe

Comments: Comments: 18 pages, Latex2e (article, amsmath, amssymb, amsthm)

Report no: nlin.SI/0601063

Kanehisa Takasaki, Takashi Takebe

Comments: 6 pages (Latex; amsmath, amssymb required), Contribution to the Proceedings of the XXIII International Conference of Differential Geometric Methods in Theoretical Physics (M.-L. Ge and W. Zhang ed., Nankai Tracts in Mathematics vol. 10, World Scientific, 2006)

Report-no: nlin.SI/0512008

Kanehisa Takasaki

Kanehisa Takasaki

("Dynamics: Frontiers in Geommetry, Analysis and Mathematical Physics", Academic exchange events of Kyoto University and Technical University of Munchen, October 7, 2005) OHP transparencies of talk [pdf]

Ryu Sasaki and Kanehisa Takasaki

J. Math. Phys. 47 (1) (2006), 012701

Comments: 18 pages, LaTeX, no figure

Report-no: YITP-05-60, hep-th/0510035

Kanehisa Takasaki

("Riemann-Hilbert problems, integrability and asymptotics", SISSA, Trieste, September 20--25, 2005) OHP transparencies of talk [pdf]

To appear in "Encyclopedia of Mathematical Sciences" Ver. 2 (Maruzen, Tokyo) [pdf]

A fully revised version of "Soliton" in Ver. 1. Contents: 1. Discovery of soliotns, 2. Inverse scattering and Lax form, 3. Conserved quantities and integrability, 4. Various equations and methods, 5. Bilinearization method, 6. KP hierarchy, 7. Other topis.

Kanehisa Takasaki

M. Noumi and K. Takasaki (ed.), ``Elliptic Integrable Systems'', Rokko Lectures in Mathematics vol. 18, pp. 289--304 (Kobe University, 2005).

Comment: contribution to proceedings of RIMS workshop "Elliptic Integrable Systems" (RIMS, 2004)

Report-no: nlin.SI/0505005

Kanehisa Takasaki

Abstract of talk at the MSJ spring meeging 2005 (Chuo University, Tokyo, March 23--30, 2005) [pdf]

Takashi Maeda, Toshio Nakatsu, Kanehisa Takasaki, Takeshi Tamakoshi

Nucl. Phys. B715 (2005) 275-303

Report-no: OU-HET 513, hep-th/0412329

Takashi Maeda, Toshio Nakatsu, Kanehisa Takasaki, Takeshi Tamakoshi

JHEP 03 (2005), 056. Report-no: OU-HET 512, hep-th/0412327

Kanehisa Takasaki

Lett. Math. Phys. 72 (3) (2005), 165--181.

Report-no: nlin.SI/0412067

Kanehisa Takasaki

Contributution to the proceedings of the RIMS workshop "Global and asymptotic analysis of differential equations in complex domain" (RIMS, Kyoto University, October 6--10, 2003) [pdf]

Kanehisa Takasaki

Article written as report for Grant-in-Aid for Scientific Research (2002--2003) [pdf]

Kanehisa Takasaki

Comments: Contribution to Faro conference "Infinite dimensional algebras and quantum integrable systems", Progress in Mathematics vol. 237, pp. 169--197 (Birkhauser, Basel/Switzerland, 2005)

Report-no: nlin.SI/0312016

Kanehisa Takasaki

Lett. Math. Phys. 67 (2) (2004), 141-152

Comments: latex2e (usepackage:amssyb), 15 pages, no figure; (v2) minor changes; (v3) typos corrected

Report-no: lin.SI/0312002

Kanehisa Takasaki

Abstract of talk at Mathematical Society Autumn Meeting 2004 (Chiba University, September 24--27, 2003). [pdf] Removed because of a serious error in the contents (Nov. 2003)

Kanehisa Takasaki

J. Math. Sci. Univ. Tokyo 11 (2004), 91--131

Comments: latex2e, 36 pp, no figure; (v2) minor changes, mostly typos; (v3) Title changed, text fully revised with new results; (v4) serious errors in section 5 corrected; (v5) proof of main results is improved; (v6) minor change in proof of Lemma 10 etc Report-no: nlin.SI/0307030

To appear in "Encyclopedic Dictionary of Mathematics" Ver. 4 (Iwanami Shoten, Tokyo) [pdf] A revised version of "Soliton" in the previous edition. Fully revised to cover such topics as 'Hamiltonian structure', 'bilinearization method', 'KP hierarchy' etc.

Kanehisa Takasaki and Takashi Takebe

Abstract of talk at Mathematical Society Annual Conference 2003 (University of Tokyo, March 23--26, 2003) [pdf]

Kanehisa Takasaki

Abstract of talk at Mathematical Society Annual Conference 2002 (University of Tokyo, March 23--26, 2003) [pdf]

Kanehisa Takasaki

Contribution to the proceedings of the workshop "In search of ideal mathematical analysis", Kyushu University, December 12 -- 14, 2002 [pdf]

Kanehisa Takasaki

Commun. Math. Phys. 241 (1) (2003), 111--142

Comments: latex2e, 41 pages no figure; Revised version (version 3), considerably shortened (56pages --> 41 pages), but some results are improved.

Report-no: nlin.SI/0206049

Comments: latex2e, 56pages, no figure

Report-no: nlin.SI/0206049

Kanehisa Takasaki

Contribution to the proceedings of the RIAM workshop "Recent topis of Nonlinear Waves and Nonlinear Dynamical Systems" (November 6--8, 2002) [pdf]

Kanehisa Takasaki

Comments: CRM Proceedings and Lecture Notes vol. 37, pp. 211--222 (AMS, Province, 2004). Contribution to the proceedings of the conference "Superintegrability in classical and quantum systems" (Montreal, September 16--22, 2002), latex2e, 15 pages, no figure

Report-no: nlin.SI/0211021

Kanehisa Takasaki

TAlk at RIMS workshop "Deformations and asymptotic analysis of differential equations" (June 3--7, 2002) [pdf]

kanehisa Takasaki and Takashi Takebe

Talk at Annual Conference of Mathematical Society of Japan (March 28 -- 31, 2002, Meiji University, Tokyo) [pdf]

Kanehisa Takasaki and Takashi Takebe

Journal of Geometry and Physics 47 (1) (2003), 1--20

Comments: 25 pages, AMS-LaTeX, no figure

Report-no: nlin.SI/0202042

Kanehisa Takasaki

TAlk at RIMS workshop "Bilinearization Method for Integrable Systems and Related Topics" (July 2--4, 2001) [pdf]

Kanehisa Takasaki

J. Math. Phys. 44 (9) (2003), 3979--3999

Comments: The manuscript published in J. Math. Phys. vol. 44 turned out to contain serious errors. A corrected version is stored in the e-print arXiv as nlin.SI/0111019 ver.6.

Report-no: nlin.SI/0111019

R. Sasaki and K. Takasaki

J.Phys. A34 (2001), 9533--9554

Comments: LaTeX2e 28 pages, no figures

Report-no: hep-th/0109008, YITP-01-60 and KUCP-0191

Saburo Kakei, Takeshi Ikeda and Kanehisa Takasaki

Ann. Henri Poincare 3 (2002), 817--845.

Comments: 26 pages, Latex2e, uses amsmath, amssymb, amsthm

Report-no: nlin.SI/0107065

Kanehisa Takasaki

Talk at Annual Conference of Mathematical Society of Japan (Keio University, March 26 - 29, 2001) [pdf]

Kanehisa Takasaki

Talk at RIMS workshop "Analysis of Painleve equations" (October 23 - 27, 2000) [pdf]

Kanehisa Takasaki

Lecture at the organized session "Applied analysis of dynamical systems -- point of view of geometry and integrable systems --", the annual conference of the Japan SIAM (Tokyo Institute of Technology, October 6 - 8, 2000) [pdf]

Kanehisa Takasaki

Phys. Lett. A283 (2001), 201--208.

Comments: latex2e using packages "amsmath and amssymb", 15 pages

Report-no: KUCP-0161, math.AG/0007073

Kanehisa Takasaki

J. Geom. Phys. 37 (2001), 291 - 306.

Comments: latex2e using packages amsmath and amssymb, 24 pages

Report-no: KUCP-153, hep-th/0005194

Kanehisa Takasaki

J. Math. Phys. 42 (3) (2001), 1443-1473.

Comments: latex2e using amsmath and amssymb packages, 40 pages, no figure

Report-no: KUCP 149, math.QA/0004118

Kanehisa Takasaki and Takeshi Ikeda

International Mathematics Research Notices 7 (2001), 329--369

Comments: LaTeX2e with amsmath and amssymb, 35 pages, no figures

Report-no: nlin.SI/0004015

Kanehisa Takasaki

Talk at Anual Conference of Mathematical Society of Japan 2000 (Waseda University, March 27 - 30, 2000) [pdf]

Kanehisa Takasaki

Plenary talk at session "Infinite Analysis", Anual Conference of Mathematical Society Japan 2000 (Waseda University, March 27 - 30, 2000) [pdf]

Kanehisa Takasaki

Based on lectures at RIMS workshop "Painleve systems, hypergeometric systems, and asymptotic analysis" (June 7 -10, 1999) and Kobe University workshop "Global analysis of Painleve equations" (October 26- 29, 1999) [pdf]

Kanehisa Takasaki

Contribution to the proceedings of RIMS workshop "Applications of Renormalization Groups to Mathematical Sciences" (July 21 - 23, 1999) [pdf]

The Whitham method extracts the slow spacetime dynamics of parameters of the carrier wave by averaging the fast oscillation. This kind of methods, called the "adiabatic approximation", is widely used in physics. A typical example is the Born-Oppenheimer approximation in quantum mechanics, whose mathematical treatment is almost the same as the Whitham averaging method. The central idea of these methods is somehow very similar to the notion of renormalization groups.

Anticipating some link with the renormalization groups, we now illustrate the Whitham averaging method for the KdV equation.

Kanehisa Takasaki

Talk at Autumn Meeting of Mathemtical Society of Japan (Hiroshima University, September 1999) [pdf]

S.P. Khastgir, R. Sasaki and Kanehisa Takasaki

Prog. Theor. Phys. 102 (4) (1999), 749-776.

Comments: LaTeX2e with amsfonts.sty, 33 pages, no figures

Report-no: YITP-99-20, KUCP-0132, hep-th/9907102

Prog. Theor. Phys. Suppl. 135 (1999), 53-74.

Comments: latex2e using amsfonts package

Report-no: KUCP-0136, hep-th/9905224

J. Math. Phys. 40 (11) (1999), 5787-5821

Comments: latex2e using amsfonts package

Report-no: KUCP-0133, math.QA/9905101

Int. J. Mod. Phys. A15 (23) (2000), 3635-3666

Comments: latex, 39pp, no figure

Report-no: KUCP-0127, hep-th/9901120

A.J. Bordner, R. Sasaki and K. Takasaki

Prog. Thero. Phys. 101 (3) (1999), 487-518.

Comments: 35 pages, LaTeX2e with amsfonts, no-figure

Report-no: YITP-98-60, KUCP-0121, hep-th/9809068

Kanehisa Takasaki

Talk at Autumn Meeting of Mathemtical Society of Japan (Osaka University, September 1998) [pdf]

This talk deals with the problem of constructuting isomonodromic
deformations of a first order matrix system
$\frac{dY}{dz} = L(z) Y$ on the torus. The matrix linear system
is assumed to have regular singularities at $N$ points
$z = t_1,\cdots,t_N$. The problem is to construct isomonodromic
deformations that leave a set of monodromy data invariant while
the position of the poles and the modulus $\tau$ being varied.
I shall present two types of such isomonodromic systems.
Both have an isospectral partner
(the elliptic Calogero-Gaudin system / the ordinary elliptic
Gaudin system), and are also related to a conformal
field theory (the ordinary WZW model / its ``twisted'' version
by Kuroki and Takebe) on a torus.