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Zbl 1010.37048
Ma, Wen-Xiu; Geng, Xianguo
Bäcklund transformations of soliton systems from symmetry constraints. (English)
[A] Coley, Alan (ed.) et al., Bäcklund and Darboux transformations. The geometry of solitons. AARMS-CRM workshop, Halifax, Canada, June 4-9, 1999. With short biographies of Albert Victor Bäcklund and Gaston Darboux. Providence, RI: American Mathematical Society (AMS). CRM Proc. Lect. Notes. 29, 313-323 (2001). ISBN 0-8218-2803-7/pbk

Summary: Binary symmetry constraints are applied to constructing Bäcklund transformations of soliton systems, both continuous and discrete. Construction of solutions to soliton systems is split into finding solutions to lower-dimensional Liouville integrable systems, which also paves a way for separation of variables and exhibits integrability by quadratures for soliton systems. Illustrative examples are provided for the KdV equation, the AKNS system of nonlinear Schrödinger equations, the Toda lattice, and the Langmuir lattice.

MSC 2000:: *37K35 Lie-Bäcklund and other transformations
35Q58 Other completely integrable PDE
37K05 Hamiltonian structures, etc.
39A10 Difference equations

Keywords: Liouville integrable systems; integrability by quadratures; KdV equation; nonlinear Schrödinger equations; Toda lattice; Langmuir lattice

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