“…In the past several years, in order to obtain exact solutions of NLS equations, many effective methods have been developed, such as the inverse scattering method, [19] the Bäcklund transformation, the Darboux transformation, [20] the Hirota method, [21] the Lie symmetry method, [22,23] the Adomian decomposition method, [24] various tanh methods, [25][26][27][28] and the generalized sub-equation expansion method. [29,30] Ever since Bluman and Cole [31] and later Olver and Rosenau [32] generalized the Lie approach to encompass symmetry transformations, lots of research referring to symmetry has been done, [33][34][35][36][37][38][39] and the study of symmetries, symmetry groups, symmetry reductions, and group invariant solutions of NLS equations has become one of the most exciting and extremely active areas of research. For example, Gagnon et al [40] studied the symmetries of a (1+1)-dimensional variable-coefficient NLS equation which involved three arbitrary complex functions of spacetime and reported that the dimension of the Lie point symmetry group G of the (1+1)-dimensional variable-coefficient NLS equation was 1 <dimG ≤ 5; Mansfield et al [41] applied a certain nonlinear generalization of Lie's linear method for finding infinitesimal symmetries to a generalization of the (3+1)-dimensional coupled NLS system; Li et al presented finite symmetry transformation groups of a (2+1)-dimensional cubic NLS equation and its corresponding cylindrical NLS equations in Ref.…”