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Эта публикация цитируется в 18 научных статьях (всего в 18 статьях)
Elliptic solutions to integrable nonlinear equations and many-body systems
A. V. Zabrodinab a Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina str. 8, Moscow, 119991, Russian Federation
b National Research University Higher School of Economics, 20 Myasnitskaya Ulitsa, Moscow 101000, Russian Federation
Аннотация:
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.
Поступила в редакцию: 03.06.2019 Принята в печать: 27.08.2019
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