Variable Separation Solutions in （1+1）-Dimensional and （3+1）-Dimensional Systems via Entangled Mapping Approach

摘要

＜正＞ In this paper, the entangled mapping approach （EMA） is applied to obtain variable separation solutions of （1+1）-dimensional and （3+1）-dimensional systems. By analysis, we firstly find that there also exists a common formula to describe suitable physical fields or potentials for these （1+1）-dimensional models such as coupled integrable dispersionless （CID） and shallow water wave equations. Moreover, we find that the variable separation solution of the （3+1）-dimensional Burgers system satisfies the completely same form as the universal quantity U1 in （2+1）-dimensional systems. The only difference is that the function q is a solution of a constraint equation and p is an arbitrary function of three independent variables.