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

Popovych, Roman O.; Ivanova, Nataliya M.; Eshraghi, Homayoon

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

Authors

Popovych, Roman O.

Ivanova, Nataliya M.

Eshraghi, Homayoon

Description

We perform the complete group classification in the class of cubic Schrödinger equations of the form $iψ_t+ψ_{xx}+ψ^2ψ^*+V(t,x)ψ=0$ 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