Quad-equations and auto-Bäcklund transformations of NLS-type systems

2013/10/22 by Dmitry K Demskoi, Demskoi, Dmitry K
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #nlin.SI

paper · pdf · doi:10.48550/arxiv.1310.5769

arxiv created 2014/01/28 · arxiv updated 2014/01/29

Abstract

Treating an integrable quad-equation along with its two generalised symmetries as a compatible system allows one to construct an auto-Bäcklund transformation for solutions of the related NLS-type system. A fixed periodic reduction of the quad-equation yields a quasi-periodic reduction of its generalised symmetries that turn them into differential constraints compatible with the NLS-type system.

Related

• Integrable Discrete Nonautonomous Quad-equations as Bäcklund Auto-transformations for Known Volterra and Toda Type Semidiscrete Equations
• Backlund Transformations of Soliton Systems from Symmetry Constraints
• From auto-Bäcklund transformations to auto-Bäcklund transformations, and torqued ABS equations
• Backlund Transformations for Darboux Integrable Differential Systems
• Invariance of the Kaup-Kupershmidt equation and triangular auto-Bäcklund transformations