Semi-direct sums of Lie algebras and discrete integrable couplings
arXiv:nlin/0603064 · doi:10.1016/j.physleta.2005.09.087
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.
arXiv comment21 pages
References in corpus (9)
- Integrable Theory of the Perturbation Equations
- Semi-direct sums of Lie algebras and discrete integrable couplings
- Algebraic Structure of Discrete Zero Curvature Equations and Master Symmetries of Discrete Evolution Equations
- The Bi-Hamiltonian Structure of the Perturbation Equations of KdV Hierarchy
- Integrable semi-discretization of the coupled nonlinear Schrödinger equations
- Complexiton Solutions of the Toda Lattice Equation
- Coupled KdV equations of Hirota-Satsuma type
- A Bi-Hamiltonian Formulation for Triangular Systems by Perturbations
- On integrability of a (2+1)-dimensional perturbed Kdv equation