Classical Lie symmetries and reductions for a generalized NLS equation in 2+1 dimensions
arXiv:1802.06608 · doi:10.1080/14029251.2017.1418053
Abstract
A non-isospectral linear problem for an integrable 2+1 generalization of the non linear Schrödinger equation, which includes dispersive terms of third and fourth order, is presented. The classical symmetries of the Lax pair and the related reductions are carefully studied. We obtain several reductions of the Lax pair that yield in some cases non-isospectral problems in 1+1 dimensions.