Noncommutative Reduction of Nonlinear Schrödinger Equation on Lie Groups

We propose a new approach that allows one to reduce nonlinear equations on Lie groups with fewer number of independent variables for finding particular solutions the equations. The main idea is apply method noncommutative integration linear part equation, which find bases in space partial differential set noncommuting symmetry operators. implemented generalized Schrödinger equation group curved local cubic nonlinearity. General formalism illustrated by example reduction nonstationary motion E(2) two-dimensional plane R2. In this case, we come usual (1+1)-dimensional soliton solution. Another provides stationary multidimensional four-dimensional exponential solvable group.