Group classification of (1+1)-Dimensional Schrödinger Equations with Potentials and Power Nonlinearities
| dc.creator | Popovych, Roman O. | |
| dc.creator | Ivanova, Nataliya M. | |
| dc.creator | Eshraghi, Homayoon | |
| dc.date | 2003-11-24 | |
| dc.date | 2004-04-08 | |
| dc.date.accessioned | 2026-07-07T06:19:08Z | |
| dc.date.available | 2026-07-07T06:19:08Z | |
| dc.description | We 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. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0311039 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0311039 | |
| dc.identifier | J.Math.Phys. 45 (2004) 3049-3057 | |
| dc.identifier | doi:10.1063/1.1765748 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/94972 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Condensed Matter | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | 35A30; 35Q55; 58J70; 81R05 | |
| dc.title | Group classification of (1+1)-Dimensional Schrödinger Equations with Potentials and Power Nonlinearities | |
| dc.type | text |