Nonlocal symmetries and interaction solutions for the (n + 1)-dimensional generalized Korteweg–de Vries equation

Abstract

The (n + 1)-dimensional generalized KdV equation is presented in this paper, and we further investigate its nonlocal symmetries by different methods. It can be seen that the symmetrical transformations obtained by different nonlocal symmetries are usually equivalent. Based on the obtained Lie point symmetry as well as the mth finite symmetrical transformations, we obtain its soliton molecules and multiple soliton solutions. Additionally, for the case of n = 4 various types of interaction solutions among solitons and periodic waves are obtained by the similarity reduction method.