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

Abstract

We perform the complete group classification in the class of cubic Schrödinger equations of the form $i{\psi }_t+{\psi }_{xx}+{\psi }^2{\psi }^{\ast }+V(t,x)\psi =0$ where $V$ is an arbitrary complex-valued potential depending on $t$ and $x$. We construct all possible inequivalent potentials for which these equations have non-trivial Lie symmetries using algebraic and compatibility methods simultaneously. Our classification essentially amends earlier works on the subject.

6 pages

References in corpus (1)

• Group classification of nonlinear Schrödinger equations

Cited by in corpus (1)

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