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The Algebro-Geometric Initial Value Problem for the Ruijsenaars-Toda Hierarchy and Quasi-Periodic Solutions
Ruijsenaars-Toda hierarchy complex-valued algebro-geometric solutions hyperelliptic curve Dubrovin-type equation Baker-Akhiezer vector
2012/4/27
We provide a detailed treatment of Ruijsenaars-Toda (RT) hierarchy with special emphasis on its the theta function representation of all algebro-geometric solutions. The basic tools involve hyperellip...
Quasi-periodic Solutions for 2k Order Wave Equations
2k order wave equations KAM theory Quasi-periodic solutions Partial Birkhoff normal form
2011/10/18
In this paper, we consider one-dimensional (1D) nonlinear 2k order wave equations under the Dirichlet boundary conditions, weher the nonlinearity f is an analytic, odd function. It is proved that for ...
Quasi-periodic solutions with Sobolev regularity of NLS on T^d with a multiplicative potential
Nonlinear Schr¨odinger equation Nash-Moser Theory
2011/1/19
We prove the existence of quasi-periodic solutions for Schr¨odinger equations with a multiplicative potential on Td, d ≥ 1, merely differentiable nonlinearities, and tangential frequencies constrained...