Group classification of (1+1)-Dimensional Schrödinger Equations with Potentials and Power Nonlinearities

Abstract

We perform the complete group classification in the class of nonlinear Schrödinger equations of the form $i{\psi }_t+{\psi }_{xx}+|\psi {|}^{\gamma }\psi +V(t,x)\psi =0$ where $V$ is an arbitrary complex-valued potential depending on $t$ and $x,$ $\gamma$ is a real non-zero constant. We construct all the possible inequivalent potentials for which these equations have non-trivial Lie symmetries using a combination of algebraic and compatibility methods. The proposed approach can be applied to solving group classification problems for a number of important classes of differential equations arising in mathematical physics.

10 pages

References in corpus (1)

• Lie Symmetries of (1+1)-Dimensional Cubic Schrödinger Equation with Potential

Cited by in corpus (1)

• New results on group classification of nonlinear diffusion-convection equations