Involutive solutions for toda and langmuir lattices through nonlinearization of lax pairs |
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Authors: | Geng Xianguo |
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Institution: | (1) Department of Mathematics, Zhengzhou University, Zhengzhou |
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Abstract: | Under the constraint determined by a relation (a n ,b n )T={f(?)} n between the reflectionless potentials and the eigenfunctions of the general discrete Schrödinger eigenvalue problem, the Lax pair of the Toda lattice is nonlinearized to be a finite-dimensional difference system and a nonlinear evolution equation, while the solution varietyN of the former is an invariant set of S-flows determined by the latter, and the constants of the motion for the algebraic system are presented.f maps the solution of the algebraic system into the solution of a certain stationary Toda equation. Similar results concerning the Langmuir lattice are given, and a relation between the two difference systems, which are the spatial parts of the nonlinearized Lax pairs of the Toda lattice and Langmuir lattice, is discussed. |
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