New periodic solitary wave solutions for the (3+1)-dimensional Jimbo-Miwa equation. (English) Zbl 1265.35323

Summary: The homoclinic test technique proposed by Z. Dai et al. [Chaos Solitons Fractals 26, No. 4, 1189–1194 (2005; Zbl 1070.35029)] for finding the periodic solitary wave solutions is further improved by expressing the quasi-solution as a nonlinear combination of trigonometric function and hyperbolic function. The effectiveness of the improved method is demonstrated by application to the well known (3+1)-dimensional Jimbo-Miwa equation with physical interest. As a result, a series of new periodic solitary wave solutions are obtained. Additionally, the propagation of the periodic solitary waves is illustrated by using the method of figure analysis.


35Q53 KdV equations (Korteweg-de Vries equations)
35B10 Periodic solutions to PDEs
35C08 Soliton solutions


Zbl 1070.35029