Modulation equations approach for solving vortex and radiation in nonlinear Schrodinger equation

Abstract

We apply the modulation theory to study the vortex and radiation solution in the two-dimensional nonlinear Schrödinger equation. The full modulation equations which describe the dynamics of the vortex and radiation separately are derived. A general algorithm is proposed to efficiently and accurately find vortices with different values of energy and spin index. The modulation equations are solved by accurate numerical method. Numerical tests and simulations of scattering are given.

arXiv comment14 pages, 7 figures

References in corpus (6)

• Mathematical theory and numerical methods for Bose-Einstein condensation
• Resonances, Radiation Damping and Instability in Hamiltonian Nonlinear Wave Equations
• Stability of spinning ring solitons of the cubic-quintic nonlinear Schrodinger equation
• A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity
• Soliton in a Well. Dynamics and Tunneling
• A modulation equations approach for numerically solving the moving soliton and radiation solutions of NLS