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Elliptic solutions to integrable nonlinear equations and many-body systems

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arxiv 1905.11383 v1 pith:QBMQETD6 submitted 2019-05-26 math-ph math.MPnlin.SI

A. Zabrodin This is my paper · ORCID
classification math-phmath.MPnlin.SI
keywords equationsintegrablemotionsolutionsellipticmany-bodynonlinearauxiliary
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We review elliptic solutions to integrable nonlinear partial differential and difference equations (KP, mKP, BKP, Toda) and derive equations of motion for poles of the solutions. The pole dynamics is given by an integrable many-body system (Calogero-Moser, Ruijsenaars-Schneider). The basic tool is the auxiliary linear problems for the wave function which yield equations of motion together with their Lax representation. We also discuss integrals of motion and properties of the spectral curves.

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  1. Elliptic solutions to matrix CKP equation

    nlin.SI 2026-08 conditional novelty 6.0 of 10

    Elliptic solutions of the matrix CKP equation have pole dynamics described by a first-order system, equations (47)-(48), generalizing the scalar CKP result.

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