Groups Analysis and Localized Solutions of the (2+1)-Dimensional Ito Equation**Supported by the Zhejiang Provincial Natural Science Foundation of China under Grant No LQ13A010014, the National Natural Science Foundation of China under Grant Nos 11326164, 11401528, 11435005 and 11375090, the Global Change Research Program of China (No 2015CB953904), the Research Fund for the Doctoral Program of Higher Education of China (No

Abstract

By means of the modified Clarkson and Kruskal (CK) direct method and the variable separation approach, we investigate the (2+1)-dimensional Ito equation which was constructed by Ito in 1980. The full symmetry group with the Kac–Moody–Virasoro algebra structure and the variable separation solutions are obtained. By selecting appropriate arbitrary functions, some special soliton excitations are shown graphically. The results presented here would be beneficial for understanding the (2+1)-dimensional Ito equation better.