Solitary wave solutions of nonlinear PDEs using Kudryashov's <i>R</i> function method
Jayita Dan, Sharmistha Sain, A. Ghose‐Choudhury, Sudip Garai
Abstract
Applications of a new function introduced by Kudryashov [Optik. 2020;206:163550] to obtain solitary wave solutions of nonlinear PDEs through their travelling wave reductions are considered. The Kudryashov function, R, satisfying a first-order second degree ODE has several features which significantly assist symbolic calculations, especially for highly dispersive nonlinear equations. A remarkable feature of the Kudryashov function R, is that its even order derivatives are polynomials in R only while its odd order derivatives turn out to be polynomials in R and Rz. The procedure has been illustrated by means of the Schrödinger–Hirota equation, a quartic NLS equation and the fifth-order Kawahara equation as examples. A comparison with the Rayleigh–Ritz variational approach has also been considered for the purposes of illustration. The results obtained here are novel and span the family of solutions for such kind of equations.