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

Roman O. Popovych·Nataliya M. Ivanova·Homayoon Eshraghi
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Abstract

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.

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BibTeXRIS

Roman O. Popovych, Nataliya M. Ivanova, Homayoon Eshraghi. 2004-04-08. Lie Symmetries of (1+1)-Dimensional Cubic Schrödinger Equation with Potential. https://arxiv.org/abs/math-ph/0310039

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