Symmetry analysis and rogue wave solutions for the (2+12+1)-dimensional nonlinear Schrödinger equation with variable coefficients

This paper addresses (2+12+1)-dimensional nonlinear Schrödinger equation (NLSE). For the special case, linear Schrödinger equation (LSE), it can be transformed into the same form of equation. On the basis of different gauge constraint, we construct potential symmetries for the LSE. And then, we consider (2+12+1)-dimensional NLSE using Lie symmetry analysis. By means of similarity transformations, we study the (2+12+1)-dimensional NLSE with nonlinearities and potentials depending on time as well as on the spatial coordinates. At last, we present the rouge wave solutions of (2+12+1)-dimensional NLSE.