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Soliton solutions and traveling wave solutions of the two-dimensional generalized nonlinear Schrödinger equations

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Abstract

In this paper, the two-dimensional generalized nonlinear Schrödinger equations are introduced with the Lax pair. The existence of the Lax pair defines integrability for the partial differential equation, so the two-dimensional generalized nonlinear Schrödinger equations are integrable. Related to this development was the understanding that certain coherent structures called solitons play a basic role in nonlinear phenomena as fluid mechanics, nonlinear optics relativity, and lattice dynamics. Via the Hirota bilinear method, bilinear forms of the two-dimensional generalized nonlinear Schrödinger equations are obtained. Based on which one- and two-soliton solutions are derived. Furthermore, to find traveling wave solutions the extended tanh method is applied. Through 2D and 3D plots, the dynamical behavior of the obtained solutions is studied. The generalized form of the nonlinear Schrödinger equations has a mathematical and physical interest because a fundamental model in the field of nonlinear science. The used methods are quite useful in the solution of nonlinear partial differential equations.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: All data included in this manuscript are available upon request by contacting with the corresponding author].

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Acknowledgements

This research is funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP08956932).

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Authors and Affiliations

  1. Faculty of Nuclear Sciences and Physical Engineering, CTU, Prague, Czech Republic

    Cestmir Burdik

  2. Department of General and Theoretical Physics, LN Gumilyov Eurasian National University, Nur-Sultan, Kazakhstan

    Gaukhar Shaikhova

  3. JSC National Company “Kazakhstan Gharysh Sapary”, Nur-Sultan, Kazakhstan

    Berik Rakhimzhanov

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  1. Cestmir Burdik
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  2. Gaukhar Shaikhova
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  3. Berik Rakhimzhanov
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Burdik, C., Shaikhova, G. & Rakhimzhanov, B. Soliton solutions and traveling wave solutions of the two-dimensional generalized nonlinear Schrödinger equations. Eur. Phys. J. Plus 136, 1095 (2021). https://doi.org/10.1140/epjp/s13360-021-02092-6

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  • DOI: https://doi.org/10.1140/epjp/s13360-021-02092-6

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