On the construction of almost general solutions for PDEs arising in nonlinear optics
Abstract
In this communication we consider the widely used nonlinear Fokas-Lenells equation, the cubic focussing nonlinear Schr\"odinger 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.
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