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

  • H. Wajahat A. RiazEmail author
Regular Article
  • 37 Downloads

Abstract.

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 \( 2 \times 2\) Lax matrices to \( 2^{N} \times 2^{N}\), 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.

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Copyright information

© Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of PunjabLahorePakistan
  2. 2.Punjab University College of Information TechnologyUniversity of the PunjabLahorePakistan

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