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

2003/10/31 by Roman O. Popovych, Nataliya M. Ivanova, Homayoon Eshraghi
Physics and Astronomy · Mathematics · #math-ph #cond-mat #hep-th #math.MP #nlin.SI #msc:35A30 #msc:35Q55 #msc:58J70 #msc:81R05

paper · pdf

published as Proceedings of Fifth International Conference "Symmetry in Nonlinear Mathematical Physics", Kyiv, Institute of Mathematics, 2004, Part 1, P. 219--224 · 6 pages

arxiv created 2004/04/08 · arxiv updated 2009/12/01

Abstract

We perform the complete group classification in the class of cubic Schrödinger equations of the form iψ_t+ψ_xx+ψ²ψ^*+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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