https://doi.org/10.1140/epjp/i2019-12597-x
Regular Article
Multicomponent nonlinear Schrödinger equation in 2+1 dimensions, its Darboux transformation and soliton solutions
1
Department of Physics, University of Punjab, Quaid-e-Azam Campus, 54590, Lahore, Pakistan
2
Punjab University College of Information Technology, University of the Punjab, Allama Iqbal Campus, 54000, Lahore, Pakistan
* e-mail: ahmed.phyy@gmail.com
Received:
17
August
2018
Accepted:
27
February
2019
Published online:
23
May
2019
In nonlinear media, propagation of pulses is generally described by multicomponent fields. In this paper, a vector (or multicomponent) (2 + 1)-dimensional nonlinear Scrödinger (NLS) equation is studied. By generalizing 
Lax matrices to 
, 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.
© Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2019
