Complete symmetry reductions, conservation laws and exact solutions for a (2+1)-dimensional nonlinear Schrodinger equation

This paper deal with a (2 + 1)-dimensional nonlinear Schrodinger (NLS) equation by the symmetry analysis, the multiplier approach and Ibragimovs conservation law method. Based on the optimal system of one dimensional subalgebras, complete similarity reduction, two types of further similarity reduction and three kinds of group-invariant solutions are obtained. Secondly, the different relationship between the NLS equation and sine-Gordon is derived. At last, some conservation laws are constructed for the NLS equation using both the multiplier method and Ibragimovs one.

Automated summary

This paper investigates a (2 + 1)-dimensional nonlinear Schrodinger (NLS) equation using symmetry analysis, the multiplier approach, and Ibragimov's conservation law method. Various similarity reductions, group-invariant solutions, and the relationship between the NLS equation and the sine-Gordon equation are explored. Additionally, conservation laws for the NLS equation are constructed using both the multiplier method and Ibragimov's approach.