Exact cross kink-wave solutions and resonance for the Jimbo–Miwa equation

In this paper, we obtain a new class of exact cross kink-wave and periodic solitary-wave solutions for Jimbo–Miwa equation by using two-soliton method, bilinear method and transforming parameters into complex ones. Moreover, we investigate singular and non-singular phenomenons of solutions. In addition, we study the resonance and non-resonance interactions between y–ty–t periodic solitons and different line solitons.