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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94972We perform the complete group classification in the class of nonlinear Schrödinger equations of the form $iψ_t+ψ_{xx}+|ψ|^γψ+V(t,x)ψ=0$ where $V$ is an arbitrary complex-valued potential depending on $t$ and $x,$ $γ$ is a real non-zero constant. We construct all the possible inequivalent potentials for which these equations have non-trivial Lie symmetries using a combination of algebraic and compatibility methods. The proposed approach can be applied to solving group classification problems for a number of important classes of differential equations arising in mathematical physics.10 pagesMathematical PhysicsCondensed MatterHigh Energy Physics - TheoryExactly Solvable and Integrable Systems35A30; 35Q55; 58J70; 81R05Group classification of (1+1)-Dimensional Schrödinger Equations with Potentials and Power Nonlinearitiestext