M. M. Gekhtman, A. Kasman, “Integrable Systems and Rank-One Conditions for Rectangular Matrices”, TMF, 133:2 (2002), 211–217; Theoret. and Math. Phys., 133:2 (2002), 1498

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Teoreticheskaya i Matematicheskaya Fizika, 2002, Volume 133, Number 2, Pages 211–217
DOI: https://doi.org/10.4213/tmf391 (Mi tmf391)

This article is cited in 13 scientific papers (total in 13 papers)

Integrable Systems and Rank-One Conditions for Rectangular Matrices

M. M. Gekhtman^a, A. Kasman^b

^a University of Notre Dame
^b College of Charleston

Full-text PDF (227 kB) Citations (13)

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DOI: https://doi.org/10.4213/tmf391

Abstract: We give a determinantal formula for tau functions of the KP hierarchy in terms of rectangular constant matrices

A

$A$ ,

B

$B$ , and

C

$C$ satisfying a rank-one condition. This result is shown to generalize and unify many previous results of different authors on constructions of tau functions for differential and difference integrable systems from square matrices satisfying rank-one conditions. In particular, its explicit special cases include Wilson's formula for tau functions of the rational KP solutions in terms of Calogero–Moser Lax matrices and our previous formula for the KP tau functions in terms of almost-intertwining matrices.

Keywords: KP hierarchies, solitions, Calogero–Moser matrices, rank-one conditions.

English version:
Theoretical and Mathematical Physics, 2002, Volume 133, Issue 2, Pages 1498–1503
DOI: https://doi.org/10.1023/A:1021142626169

Bibliographic databases:

Language: Russian

Citation: M. M. Gekhtman, A. Kasman, “Integrable Systems and Rank-One Conditions for Rectangular Matrices”, TMF, 133:2 (2002), 211–217; Theoret. and Math. Phys., 133:2 (2002), 1498–1503

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf391

https://doi.org/10.4213/tmf391

https://www.mathnet.ru/eng/tmf/v133/i2/p211

This publication is cited in the following 13 articles:

Vekslerchik V.E., “Dark Solitons of the Gross-Neveu Model”, Prog. Theor. Exp. Phys., 2022:2 (2022), 023A01
Chuanzhong Li, “Finite-dimensional tau functions of the universal character hierarchy”, Theoret. and Math. Phys., 206:3 (2021), 321–334
Harnad J., Balogh F., “Tau Functions and Their Applications”, Tau Functions and Their Applications, Cambridge Monographs on Mathematical Physics, Cambridge Univ Press, 2021, 1–521
V. E. Vekslerchik, “Solitons of Some Nonlinear Sigma-Like Models”, SIGMA, 16 (2020), 144, 13 pp.
Vekslerchik V.E., “Solitons of the (2+2)-Dimensional Toda Lattice”, J. Phys. A-Math. Theor., 52:4 (2019), 045202
Vekslerchik V.E., “Soliton Fay Identities: II. Bright Soliton Case”, J. Phys. A-Math. Theor., 48:44 (2015), 445204
Vekslerchik V.E., “Soliton Fay Identities: i. Dark Soliton Case”, J. Phys. A-Math. Theor., 47:41 (2014), 415202
Balogh F., Fonseca T., Harnad J., “Finite Dimensional Kadomtsev-Petviashvili Tau-Functions. i. Finite Grassmannians”, J. Math. Phys., 55:8 (2014), 083517
Xu D.-d. Zhang D.-j. Zhao S.-l., “The Sylvester Equation and Integrable Equations: i. the Korteweg-de Vries System and sine-Gordon Equation”, J. Nonlinear Math. Phys., 21:3 (2014), 382–406
Iliev, P, “Rational Ruijsenaars-Schneider hierarchy and bispectral difference operators”, Physica D-Nonlinear Phenomena, 229:2 (2007), 184
Gekhtman, M, “Tau-functions, Grassmannians and rank one conditions”, Journal of Computational and Applied Mathematics, 202:1 (2007), 80
Gekhtman, M, “On KP generators and the geometry of the HBDE”, Journal of Geometry and Physics, 56:2 (2006), 282
Dimakis, A, “From nonassociativity to solutions of the KP hierarchy”, Czechoslovak Journal of Physics, 56:10–11 (2006), 1123

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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