Semi-direct sums of Lie algebras and continuous integrable couplings

2005/11/09 by Wen-Xiu Ma, Wen‐Xiu Ma, Xi-Xiang Xu +1
Chemistry · Physics and Astronomy · #Molecular spectroscopy and chirality #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #nlin.SI

paper · pdf · doi:10.1016/j.physleta.2005.09.087

21 pages

openalex publication_date 2005/11/09 · arxiv created 2006/03/27 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

A relation between semi-direct sums of Lie algebras and integrable couplings of lattice equations is established, and a practicable way to construct integrable couplings is further proposed. An application of the resulting general theory to the generalized Toda spectral problem yields two classes of integrable couplings for the generalized Toda hierarchy of lattice equations. The construction of integrable couplings using semi-direct sums of Lie algebras provides a good source of information on complete classification of integrable lattice equations.

Citations

• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• On Integrability of a (2+1)-Dimensional Perturbed KdV Equation
• Integrable semi-discretization of the coupled nonlinear Schrödinger equations