Solitons and other solutions of the long-short wave equation

Abstract

Purpose – The purpose of this paper is to discuss the integrability studies to the long-short wave equation that is studied in the context of shallow water waves. There are several integration tools that are applied to obtain the soliton and other solutions to the equation. The integration techniques are traveling waves, exp-function method, G′/G-expansion method and several others. Design/methodology/approach – The design of the paper is structured with an introduction to the model. First the traveling wave hypothesis approach leads to the waves of permanent form. This eventually leads to the formulation of other approaches that conforms to the expected results. Findings – The findings are a spectrum of solutions that lead to the clearer understanding of the physical phenomena of long-short waves. There are several constraint conditions that fall out naturally from the solutions. These poses the restrictions for the existence of the soliton solutions. Originality/value – The results are new and are sharp with Lie symmetry analysis and other advanced integration techniques in place. These lead to the connection between these integration approaches.