Higher dimensional integrable Vakhnenko–Parkes equation: multiple soliton solutions

Abstract

Purpose This study aims to develop a new (3 + 1)-dimensional Painlevé-integrable extended Vakhnenko–Parkes equation. The author formally derives multiple soliton solutions for this developed model. Design/methodology/approach The study used the simplified Hirota’s method for deriving multiple soliton solutions. Findings The study finds that the developed (3 + 1)-dimensional Vakhnenko–Parkes model exhibits complete integrability in analogy with the standard Vakhnenko–Parkes equation. Research limitations/implications This study addresses the integrability features of this model via using the Painlevé analysis. The study also reports multiple soliton solutions for this equation by using the simplified Hirota’s method. Practical implications The work reports extension of the (1 + 1)-dimensional standard equation to a (3 + 1)-dimensional model. Social implications The work presents useful algorithms for constructing new integrable equations and for handling these equations. Originality/value The paper presents an original work with newly developed integrable equation and shows useful findings.