Non-classical Symmetry Analysis Of A Class Of Nonlinear Lattice Equations

Nonlinear lattice dynamics has a wide range of applications in the field of physics,and its mathematical models often appear in the form of nonlinear differentialdifference equations.We introduce a method that can obtain the symmetries of nonlinear lattice equations,namely nonclassical symmetry of the differential-difference equations.This symmetry method requires that the group action is invariant on the common solution sets of the differential-difference equations and the invariant surface condition,resulting in more forms of symmetries.The advantage of this method is the calculation amount becomes smaller,which is convenient for calculation,and more forms of symmetries of the differential-difference equations can be obtained if the equations can be reduced.In this paper,the(2+1)-dimensional Toda lattice equation and the(2+1)-dimensional Toda-like lattice equation are taken for example.The nonclassical symmetry method is used to obtain the corresponding symmetries and reduction equations.