A remark on a variable-coefficient Bernoulli equation based on auxiliary -equation method for nonlinear physical systems

TL;DR

This paper extends the auxiliary equation method by introducing a variable-coefficient Bernoulli equation, leading to new exact travelling wave solutions for nonlinear physical systems, surpassing the classical Bernoulli equation in solution diversity.

Contribution

It develops a new class of auxiliary equations, the variable-coefficient Bernoulli type, to generate more diverse solutions for nonlinear PDEs in physical systems.

Findings

New exact solutions for nonlinear PDEs derived

Variable-coefficient Bernoulli equation produces more solutions than classical

Application to physical systems demonstrates practical relevance

Abstract

It is well recognized that in auxiliary equation methods, the exact solutions of different types of auxiliary equations may produce new types of exact travelling wave solutions to nonlinear partial differential equations in hand. In this study, we extend the class of auxiliary equations of classical Bernoulli equation which considered by various researchers [27, 31, 32, 33, 34, 35] to a variable-coefficient Bernoulli type equation. The proposed variable-coefficient Bernoulli type auxiliary equation produces many new solutions comparing to classical Bernoulli equation which produce two solutions only. Consequently, we introduce new exact travelling wave solutions of some physical systems in terms of these new solutions of the variable-coefficient Bernoulli type equation.