Envelope solitons for generalized forms of the phi-four equation

Abstract

We consider two variants of the generalized phi-four equation with arbitrary constant coefficients and general values of the exponents in the dissipation and nonlinear terms. By using solitary wave ansatze in terms of sechp(x) and tanhp(x) functions respectively, we find the non-topological (bright) as well as topological (dark) soliton solutions for the considered models. The physical parameters in the soliton solutions are obtained as a function of the dependent model coefficients. The conditions of existence of solitons are presented. Further, we show that the obtained soliton solutions depend on the exponent of the wave function u(x,t), positive or negative, and on all the dependent model coefficients as well.