The soliton solutions and combined solutions of a high-dimensional wave soliton equation

Abstract

Abstract In this paper, a high-dimensional wave soliton equation is considered and the simple Hirota method and bilinear backlund transformation are applied to construct the new soliton solutions, lump soliton solutions, breather solutions and their combined solutions. Then, through long-wave limit method and appropriate parameter constraints, one-soliton, one-breather, combined soliton-lump and lump-breather and soliton-breather solutions to nonlinear wave equation are obtained. Moreover, the physical interaction and frontal collision phenomena to the solutions of this equation are explored. In addition, a kind of hyperbolic and trigonometric ansatz is employed to derive other solutions such as kink soliton solution, periodic solutions for the high-dimensional wave equation.The obtained results verify the proposed solutions.