Reduction groups and related integrable difference systems of nonlinear Schrödinger type

2015/03/22 by S. Konstantinou-Rizos, A. V. Mikhailov, P. Xenitidis · 31 citations
Computer Science · Mathematics · Physics and Astronomy · #Group (periodic table) #Integrable system #Lax pair #Nonlinear Waves and Solitons #Nonlinear system #Numerical methods for differential equations #Polynomial and algebraic computation #Reduction (mathematics) #Scalar (mathematics) #Type (biology) #nlin.SI

paper · pdf · doi:10.1063/1.4928048

published in Journal of Mathematical Physics 56(8) (American Institute of Physics) · 25 pages

arxiv created 2015/03/22 · openalex publication_date 2015/08/01 · arxiv updated 2015/09/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We extend the reduction group method to the Lax-Darboux schemes associated with nonlinear Schrödinger type equations. We consider all possible finite reduction groups and construct corresponding Lax operators, Darboux transformations, hierarchies of integrable differential-difference equations, integrable partial difference systems, and associated scalar partial difference equations.

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• Noncommutative NLS systems: Darboux--Bäcklund transformations and integrable discretisations
• On matrix Lax representations for (1+1)-dimensional evolutionary differential-difference equations

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