Compactons, solitons and periodic solutions for variants of the KdV and the KP equations

Studying solitons and solitons with compact support is of important significance in nonlinear phenomena. In this paper we study nonlinear variants of the KdV and the KP equations with positive and negative exponents. We employ the sine-cosine algorithm to back up our analysis. Exact solutions with compactons, solitons, solitary patterns, and periodic structures are obtained for these variants.