Elliptic solutions to integrable nonlinear equations and many-body systems

JOURNAL OF GEOMETRY AND PHYSICS

卷:146

Article

Zabrodin, A.^1,2 

[1] Natl Res Univ Higher Sch Econ, 20 Myasnitskaya Ulitsa, Moscow 101000, Russia

[2] Russian Acad Sci, Steklov Math Inst, Gubkina Str 8, Moscow 119991, Russia

关键词: Integrable equations;    Elliptic solutions;    Dynamics of poles;    Integrable many-body systems;   

DOI  :  10.1016/j.geomphys.2019.103506

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free