Multicomponent nonlinear Schrodinger equation in 2+1 dimensions, its Darboux transformation and soliton solutions

摘要

.In nonlinear media, propagation of pulses is generally described by multicomponent fields. In this paper, a vector (or multicomponent) (2 + 1)-dimensional nonlinear Scrodinger (NLS) equation is studied. By generalizing 2x2 Lax matrices to 2Nx2N, we derive the Lax pair for the multicomponent (2 + 1)-dimensional NLS equation. We construct the Darboux matrix for the system and obtain K-soliton solutions and express these solutions in terms of quasideterminants. Within the framework of quasideterminants and symbolic computation, we compute 1-, 2- and 3-soliton solutions for (2 + 1)-dimensional and coupled (2 + 1)-dimensional NLS equations. Graphically, it has been shown that solitons of the (2 + 1)-dimensional and coupled (2 + 1)-dimensional NLS equations propagate with different velocities in the xt-, yt-, and xy-plane, but keeping the amplitude and width unchanged.