Exact solitary wave solutions of coupled nonlinear evolution equations using MACSYMA

W Hereman - Computer Physics Communications, 1991 - Elsevier
A direct series method to find exact travelling wave solutions of nonlinear PDEs is applied to
Hirota's system of coupled Korteweg-de Vries equations and to the sine-Gordon equation …

Exact N-envelope-soliton solutions of the Hirota equation

JJ Shu - arxiv preprint arxiv:1403.3645, 2014 - arxiv.org
We discuss some properties of the soliton equations of the type, partial derivative u/partial
derivative t= S [u,(u) over bar], where S is a nonlinear operator differential in x, and present …

Bidifferential calculus, matrix SIT and sine-Gordon equations

A Dimakis, N Kanning, F Müller-Hoissen - arxiv preprint arxiv:1011.1737, 2010 - arxiv.org
We express a matrix version of the self-induced transparency (SIT) equations in the
bidifferential calculus framework. An infinite family of exact solutions is then obtained by …