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

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.

Dynamics of breather waves, lump-kink solutions and interaction solutions for a (3+1)-dimensional generalized shallow water waves equation

“…To investigate new kinds of interaction solutions of equation (1), a “rational-cosh-cos-type” test function (He et al , 2018; Liu and Gao, 2022) is introduced as follows: where: where a i ( i = 1,2,…,9), k i ( i = 1,2,3,4), p and q are real constants, m i ( i = 1,2,3,4) are real or pure imaginary constants. Substituting equation (16) with equation (17) into equation (4), three constraint sets are obtained.…”

“…To investigate new kinds of interaction solutions of equation ( 1), a "rational-cosh-cos-type" test function (He et al, 2018;Liu and Gao, 2022) is introduced as follows:…”