On the construction of almost general solutions for PDEs arising in nonlinear optics

TL;DR

This paper develops methods to construct nearly general solutions for certain nonlinear PDEs in optics, using traveling wave ansatz and elliptic functions, enabling derivation of solitary wave solutions.

Contribution

It introduces a systematic approach to find almost general solutions for nonlinear PDEs in optics using elliptic functions and traveling wave ansatz.

Findings

Constructed solutions expressed via Jacobi elliptic sine functions.

Derived solitary wave solutions by imposing conditions on polynomial roots.

Applied method to multiple nonlinear PDEs in optics.

Abstract

In this communication we consider the widely used nonlinear Fokas-Lenells equation, the cubic focussing nonlinear Schr\"{o}dinger equation in (2+1)-dimensions and the coupled Drinfel'd-Sokolov-Wilson equation and attempt to construct almost general solutions for the envelope of the wave packet by means of the travelling wave ansatz. The obtained solutions have been expressed in terms of Jacobi elliptic sine function from which one can obtain the solitary wave (particular) solutions by imposing appropriate conditions on the roots of certain quartic polynomials.