(1) Department of Physics, Shanghai Jiao Tong University, Shanghai, 200240, China;(2) Department of Physics, Ningbo University, Ningbo, 315211, China;(3) School of Mathematics, Fudan University, Shanghai, 200433, China
Abstract:
The multi-linear variable separation approach is reviewed in this article. The method has been recently established and successfully
solved a large number of nonlinear systems. One of the most exciting findings is that the basic multi-linear variable separation
solution can be expressed by a universal formula including two (1+1)-dimensional functions, and at least one is arbitrary
for integrable systems. Furthermore, the method has been extended in two different ways so as to enroll more low dimensional
functions in the solution.