Motion of 2D Schrödinger solitary waves in the presence of random external potentials. (English) Zbl 1064.35195
Summary: The trapping of 2D localised solutions that may exist for a generalised \((2+1)\)-dimensional nonlinear Schrödinger equation with a random external potential is analysed. The method used is based on the stability properties of a system of stochastic ordinary differential equations describing the motion of the soliton center. The model has a wide range of applications including nonlinear optics and Bose-Einstein condensation.
MSC:
35Q55 | NLS equations (nonlinear Schrödinger equations) |
78A48 | Composite media; random media in optics and electromagnetic theory |
37K40 | Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems |