A FAMILY OF EXACT TRAVELING-WAVE SOLUTIONS TO NONLINEAR EVOLUTION ANDWAVE-EQUATIONS

A family {q} of the multicomponent special functions is defined for ob taining the exact travelling wave solutions to nonlinear evolution and wave equations. It is shown that the functions q(n) 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 t he exact multicomponent travelling wave solutions to a quasilinear evo lution equation are given. An efficiency of the method based on q-func tions is demonstrated on several classes of the nonlinear partial diff erential equations. (C) 1997 American Institute of Physics.