New (3+1)-dimensional integrable fourth-order nonlinear equation: lumps and multiple soliton solutions

Abstract

PurposeThis paper aims to introduce a new (3 + 1)-dimensional fourth-order integrable equation characterized by second-order derivative in time t. The new equation models both right- and left-going waves in a like manner to the Boussinesq equation.Design/methodology/approachThis formally uses the simplified Hirota’s method and lump schemes for determining multiple soliton solutions and lump solutions, which are rationally localized in all directions in space.FindingsThis paper confirms the complete integrability of the newly developed (3 + 1)-dimensional model in the Painevé sense.Research limitations/implicationsThis paper addresses the integrability features of this model via using the Painlevé analysis.Practical implicationsThis paper presents a variety of lump solutions via using a variety of numerical values of the included parameters.Social implicationsThis work formally furnishes useful algorithms for extending integrable equations and for the determination of lump solutions.Originality/valueTo the best of the author’s knowledge, this paper introduces an original work with newly developed integrable equation and shows useful findings of solitons and lump solutions.