Solitary wave solutions of nonlinear PDEs using Kudryashov's R function method

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 R-z . The procedure has been illustrated by means of the Schrodinger-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.

Automated summary

The new function introduced by Kudryashov is applied to obtain solitary wave solutions of nonlinear PDEs through travelling wave reductions. The function R has unique features that significantly assist symbolic calculations, especially for highly dispersive nonlinear equations. Illustrated through examples like the Schrodinger-Hirota equation, a quartic NLS equation, and the fifth-order Kawahara equation, this method provides novel solutions for such equations and compares favorably with the Rayleigh-Ritz variational approach.