Groups Analysis and Localized Solutions of the (2+1)-Dimensional Ito Equation

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.