New Compacton-Like and Solitary Pattern-Like Solutionsof (2+1)-Dimensional Generalization of Modified KdVEquation**The project supported by Natural Science Foundation of ZhejiangProvince of China under Grant No. Y604056, Postdoctoral Science Foundation of China,National Natural Science Foundationof China under Grant No. 10401039, the State Key Basic Research Projectof China under Grant No. 2004CB318000, and the ScientificResearch Foundation for the Returned Overseas Chinese Scholarsof the

Abstract

Recently some (1+1)-dimensional nonlinear wave equations with linearlydispersive terms were shown to possess compacton-like and solitarypattern-like solutions. In this paper, with the aid of Maple,new solutions of (2+1)-dimensional generalizationof mKdV equation, which is of only linearly dispersive terms, are investigatedusing three new transformations. As a consequence, it is shownthat this (2+1)-dimensional equation also possesses newcompacton-like solutions and solitary pattern-like solutions.