Backlund Transformations of Soliton Systems from Symmetry Constraints

2001/07/31 by Wen-Xiu Ma, Xianguo Geng, Ma, Wen-Xiu +1
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0107071

11 pages, to appear in CRM Proceedings of AARMS-CRM Workshop on Bäcklund & Darboux Transformations (1999)

arxiv created 2001/07/31 · arxiv updated 2009/11/30

Abstract

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.

Related

• Binary Bargmann Symmetry Constraints of Soliton Equations
• The Theory of Binary Nonlinearization and Its Applications to Soliton Equations
• On an integrable system related to the relativistic Toda lattice -Bäcklund transformation and integrable discretization
• Gauge-Theoretical Method in Solving Zero-curvature Equations III --Gauge Theoretical Method and the Bäcklund Transformations for Solitons--
• Non-symmetry constraints of the AKNS system yielding integrable Hamiltonian systems