Exact solutions of the cubic and quintic nonlinear Schrödinger equation for a cylindrical geometry
- 1 January 1989
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 39 (1) , 296-306
- https://doi.org/10.1103/physreva.39.296
Abstract
Exact solutions of the nonlinear Schrödinger equation +Δψ=ψ/B +ψ‖ψ+ψ‖ψ, for which initial conditions can be imposed on a cylinder, are presented. A symmetry group of the equation is used to reduce it to an ordinary differential equation which is then solved with the help of a singularity analysis. Solutions are obtained in terms of elementary functions, Jacobi elliptic functions, and Painlevé transcendents.
Keywords
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