Elliptic solutions to integrable nonlinear equations and many-body systems
arXiv:1905.11383 · doi:10.1016/j.geomphys.2019.103506
Abstract
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.
arXiv comment38 pages, no figures. arXiv admin note: substantial text overlap with arXiv:1903.00968
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- Elliptic families of solutions to constrained Toda hierarchy
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- How Calogero-Moser particles can stick together
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- Elliptic solutions to Toda lattice hierarchy and elliptic Ruijsenaars-Schneider model
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