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Implicit Solitary Waves for One of the Generalized Nonlinear Schrödinger Equations

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  • Nikolay A. Kudryashov

    (MEPhI (Moscow Engineering Physics Institute), National Research Nuclear University, 31 Kashirskoe Shosse, 115409 Moscow, Russia
    National Research Center “Kurchatov Center”, 1 Akademika Kurchatova Sq., 123182, Moscow, Russia)

Abstract

Application of transformations for dependent and independent variables is used for finding solitary wave solutions of the generalized Schrödinger equations. This new form of equation can be considered as the model for the description of propagation pulse in a nonlinear optics. The method for finding solutions of equation is given in the general case. Solitary waves of equation are obtained as implicit function taking into account the transformation of variables.

Suggested Citation

  • Nikolay A. Kudryashov, 2021. "Implicit Solitary Waves for One of the Generalized Nonlinear Schrödinger Equations," Mathematics, MDPI, vol. 9(23), pages 1-9, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3024-:d:688108
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    References listed on IDEAS

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    1. Kudryashov, Nikolay A., 2020. "Highly dispersive solitary wave solutions of perturbed nonlinear Schrödinger equations," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    2. Ekici, Mehmet & Sonmezoglu, Abdullah & Biswas, Anjan, 2021. "Stationary optical solitons with Kudryashov’s laws of refractive index," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    3. Kudryashov, Nikolay A., 2019. "Exact solutions of the equation for surface waves in a convecting fluid," Applied Mathematics and Computation, Elsevier, vol. 344, pages 97-106.
    4. Zayed, Elsayed M.E. & Alngar, Mohamed E.M. & Biswas, Anjan & Asma, Mir & Ekici, Mehmet & Alzahrani, Abdullah K. & Belic, Milivoj R., 2020. "Optical solitons and conservation laws with generalized Kudryashov’s law of refractive index," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
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    Cited by:

    1. Hu, Xiang & Yin, Zhixiang, 2022. "A study of the pulse propagation with a generalized Kudryashov equation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Nikolay A. Kudryashov, 2022. "Optical Solitons of the Generalized Nonlinear Schrödinger Equation with Kerr Nonlinearity and Dispersion of Unrestricted Order," Mathematics, MDPI, vol. 10(18), pages 1-9, September.

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