2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57537We 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 pagesMathematical PhysicsCondensed MatterHigh Energy Physics - TheoryExactly Solvable and Integrable Systems35A30; 35Q55; 58J70; 81R05text