A new class of solutions to a generalized nonlinear Schrodinger equation

In this paper we compute new classes of symmetry reduction and associated exact solutions of a generalized nonlinear Schrodinger equation (GNLS), the generalized terms modelling dispersion and scattering. Several authors have obtained symmetry reductions of one-, two- and three-dimensional nonlinear Schrodinger equations; in all cases to date reductions have been based on a real new independent variable. In this paper we compute reductions in which the new independent variable is complex. We seek new reductions from a two-dimensional GNLS to a PDE in two independent variables and also reductions to ODEs. Five new classes of reduction are found.