New approach for soliton solutions for the (2 + 1)-dimensional KdV equation describing shallow water wave

Abstract

Purpose The purpose of this study is to produce families of exact soliton solutions (2+1)-dimensional Korteweg-de Vries (KdV) equation, that describes shallow water waves, using an ansätze approach. Design/methodology/approach This article aims to introduce a recently developed ansätze for creating soliton and travelling wave solutions to nonlinear nonintegrable partial differential equations, especially those with physical significance. Findings A recently developed ansätze solution was used to successfully construct soliton solutions to the (2 + 1)-dimensional KdV equation. This straightforward method is an alternative to the Painleve test analysis, yielding similar results. The strategy demonstrated the existence of a single soliton solution, also known as a localized wave or bright soliton, as well as singular solutions or kink solitons. Originality/value The ansätze solution used to construct soliton solutions to the (2 + 1)-dimensional KdV equation is novel. New soliton solutions were also obtained.