Modified simple equation technique for first-extended fifth-order nonlinear equation, medium equal width equation and Caudrey–Dodd–Gibbon equation

Abstract

AbstractIn order to figure out the interior construction and intricacy of nonlinear physical events in the real world, exact solutions and traveling wave solutions of the nonlinear equations are very crucial. The modified simple equation technique is a powerful and proficient technique for investigating traveling wave solutions of nonlinear equations found in applied mathematics, science and engineering. Exact solutions and traveling wave solutions allow researchers to predict the activities of the system under different circumstances. The aforementioned technique is utilized to investigate exact and traveling wave solutions for three important equations: the first-extended fifth-order nonlinear equation, the nonlinear medium equal width equation, and the Caudrey–Dodd–Gibbon equation. Here we obtained kink shape solution, singular kink, periodic solutions, bell shape solution and compacton solutions. The above approach performs better than other approaches nowadays in use in terms of consistency, competence, and effectiveness.