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

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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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Authors and Affiliations

  1. Department of Physics, University of Punjab, Quaid-e-Azam Campus, 54590, Lahore, Pakistan

    H. Wajahat A. Riaz

  2. Punjab University College of Information Technology, University of the Punjab, Allama Iqbal Campus, 54000, Lahore, Pakistan

    H. Wajahat A. Riaz

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  1. H. Wajahat A. Riaz
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Correspondence to H. Wajahat A. Riaz.

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Riaz, H.W.A. Multicomponent nonlinear Schrödinger equation in 2+1 dimensions, its Darboux transformation and soliton solutions. Eur. Phys. J. Plus 134, 222 (2019). https://doi.org/10.1140/epjp/i2019-12597-x

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  • DOI: https://doi.org/10.1140/epjp/i2019-12597-x

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