A family of exact travelling wave solutions to nonlinear evolution and wave equations

Publisher Website
Google Scholar
Abstract
A family {q} of the multicomponent special functions is defined for obtaining the exact travelling wave solutions to nonlinear evolution and wave equations. It is shown that the functions qn from {q} for some n=2,4,… are closely related to the special unitary groups SU(n). The necessary and sufficient conditions for existence of a family of the exact multicomponent travelling wave solutions to a quasilinear evolution equation are given. An efficiency of the method based on q-functions is demonstrated on several classes of the nonlinear partial differential equations.