Generalized forms of the phi-four equation with compactons, solitons and periodic solutions

In this paper we study two generalized forms of the phi-four equation. Compactons: solitons with the absence of infinite wings, conventional solitons: nonlinear localized waves with infinite support, solitary patterns solutions having infinite slopes or cusps, and plane periodic solutions are developed. The sine–cosine ansatz can be fruitfully employed to develop these physical solutions. The qualitative change in the physical structure of the obtained solutions is shown to depend mainly on the exponent of the wave function u(x,t), positive or negative, and on the coefficient of the term (un)xx as well.