Virasoro symmetry subalgebra, multi-linear variable separation solutions and localized excitations of higher-dimensional differential-difference models

Abstract

Seeking for higher-dimensional integrable models is important in nonlinear science. By using the infinite dimensions Virasoro symmetry subalgebra［σ(f1),σ(f2)］=σ(f′1f2-f′2f1) and prolongation theory, many higher-dimensional models can be derived. By means of a concrete realization, some higher-dimensional differential integrable models with infinite dimensions Virasoro symmetry subalgebra can be obtained. In this paper, this method is extended to obtain differential-difference models and a (3+1)-dimensional Toda-like lattice which is week multi-linear variable separation solvable (MLVSS) model is derived. In addition, this model can be symmetry reduced to a (2+1)-dimensional special Toda lattice which is a MLVSS model. A (1+1)-dimensional MLVSS Toda lattice also can be obtained. Because some arbitrary functions are included, abundant new localized excitations such as dromion solution, lump solution, ring soliton, breather instanton et al can be found by selecting appropriate functions.