Novel dynamical behaviors of interaction solutions of the new (3+1)-dimensional integrable fourth-order nonlinear equation

Abstract

Abstract In this paper, the breather wave, rouge wave and interaction solutions of lumps and various solitary waves of the (3+1)-dimensional integrable fourth-order nonlinear equation are discussed. With the aid of the extended homoclinc test, the breather wave and rouge wave are gained. Subsequently, the interaction solutions between a lump wave and 1-kink soliton or 2-kink soliton are studied. In addition, four types of interaction solutions between lump, kink and periodic waves via a “rational-cosh-cos” type test function are constructed. Moreover, the dynamical characteristics of these obtained solutions are displayed using graphical analysis.