A novel and efficient method for obtaining Hirota’s bilinear form for the nonlinear evolution equation in (n+1) dimensions

Abstract

Bilinearization of nonlinear partial differential equations (PDEs) is essential in the Hirota method, which is a widely used and robust mathematical tool for finding soliton solutions of nonlinear PDEs in a variety of fields, including nonlinear dynamics, mathematical physics, and engineering sciences. We present a novel systematic computational approach for determining the bilinear form of a class of nonlinear PDEs in this article. It can be easily implemented in symbolic system software like Mathematica, Matlab, and Maple because of its simplicity. The proven results are obtained by using a developed method in Mathematica and applying a logarithmic transformation to the dependent variable. Finally, the findings validate the implemented technique’s competence, productivity, and dependability. The approach is a useful, authentic, and simple mathematical tool for calculating multiple soliton solutions to nonlinear evolution equations encountered in nonlinear sciences, plasma physics, ocean engineering, applied mathematics, and fluid dynamics. • This paper introduces a new systematic computational approach for constructing bilinear forms for nonlinear PDEs. • The given approach can handle a class of (n+1)-dimensional nonlinear PDEs. • Various examples of well-known nonlinear evolution equations up to the (4+1)-dimension are shown. • The results of various nonlinear equations are provided using the proposed method.