New non-traveling wave solutions for the (2+1)-dimensional variable coefficients Date-Jimbo-Kashiwara-Miwa equation

Abstract

In the paper, we mainly study the (2+1)-dimensional variable coefficients Date-Jimbo-Kashiwara-Miwa equation (VC-DJKM equation) by combining the extended homoclinic test approach and the generalized variable separation method. Applying this thought and with the aid of symbolic computation, we present thirty six kinds of new exact non-traveling wave solutions of the (2+1)-dimensional VC-DJKM equation including kink-like solution, singular solitary wave-like solution, periodic solitary wave-like solution, kinky breather wave-like solution, and so on. These results all have a like-parabolic tail which reveals the complex structure of solution and maybe give a prediction of physical phenomenon. The generalized variable separation method greatly enriches the types and structures of solutions. Moreover, when some functions in the generalized variable separation form take 0 or 1, it will degenerate into the variable separation form of multiplication or addition. As the special case of VC-DJKM equation, the corresponding results of the (2+1)-dimensional DJKM equation with constant coefficients are also given.