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

Abstract

PurposeThe 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/approachThis 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.FindingsA 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/valueThe ansätze solution used to construct soliton solutions to the (2 + 1)-dimensional KdV equation is novel. New soliton solutions were also obtained.