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Highly dispersive solitary wave solutions of perturbed nonlinear Schrödinger equations

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  • Kudryashov, Nikolay A.

Abstract

Hierarchy of the perturbed nonlinear Schrödinger equations is considered. Nonlinear differential equations of this hierarchy contain higher orders and can be used for description of highly dispersive optical solutions. A new approach for finding solitary wave solutions of high-order nonlinear differential equations is presented. This approach allows us to significantly simplify symbolic calculations. The main idea of the method is that we use expressions of the dependent variable and its derivatives in the differential equation the polynomial form of the solitary wave. We find optical solitons with high dispersion order for nonlinear perturbed Schrodinger equations of the fourth, sixth, eighth, tenth and twelfth orders.

Suggested Citation

  • Kudryashov, Nikolay A., 2020. "Highly dispersive solitary wave solutions of perturbed nonlinear Schrödinger equations," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    • Handle: RePEc:eee:apmaco:v:371:y:2020:i:c:s0096300319309646
    DOI: 10.1016/j.amc.2019.124972
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    References listed on IDEAS

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    1. Kudryashov, Nikolai A., 2005. "Simplest equation method to look for exact solutions of nonlinear differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1217-1231.
    2. 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.
    3. Kudryashov, Nikolay A., 2019. "Lax pair and first integrals of the traveling wave reduction for the KdV hierarchy," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 323-330.
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    Citations

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    Cited by:

    1. Elsayed M. E. Zayed & Khaled A. Gepreel & Mahmoud El-Horbaty & Anjan Biswas & Yakup Yıldırım & Hashim M. Alshehri, 2021. "Highly Dispersive Optical Solitons with Complex Ginzburg–Landau Equation Having Six Nonlinear Forms," Mathematics, MDPI, vol. 9(24), pages 1-19, December.
    2. Kudryashov, Nikolay A. & Nifontov, Daniil R., 2023. "Conservation laws and Hamiltonians of the mathematical model with unrestricted dispersion and polynomial nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    3. Ekici, Mehmet, 2022. "Kinky breathers, W-shaped and multi-peak soliton interactions for Kudryashov's quintuple power-law coupled with dual form of non-local refractive index structure," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    4. 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.
    5. Oswaldo González-Gaxiola & Anjan Biswas & Yakup Yıldırım & Luminita Moraru, 2022. "Highly Dispersive Optical Solitons in Birefringent Fibers with Polynomial Law of Nonlinear Refractive Index by Laplace–Adomian Decomposition," Mathematics, MDPI, vol. 10(9), pages 1-12, May.
    6. Nikolay A. Kudryashov, 2021. "Implicit Solitary Waves for One of the Generalized Nonlinear Schrödinger Equations," Mathematics, MDPI, vol. 9(23), pages 1-9, November.
    7. Kudryashov, Nikolay A., 2020. "First integrals and general solution of the complex Ginzburg-Landau equation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    8. El-Ganaini, Shoukry & Kumar, Sachin, 2023. "Symbolic computation to construct new soliton solutions and dynamical behaviors of various wave structures for two different extended and generalized nonlinear Schrödinger equations using the new impr," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 28-56.
    9. Xu, Guoan & Zhang, Yi & Li, Jibin, 2022. "Exact solitary wave and periodic-peakon solutions of the complex Ginzburg–Landau equation: Dynamical system approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 157-167.
    10. Kudryashov, Nikolay A., 2020. "Optical solitons of model with integrable equation for wave packet envelope," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    11. Boutabba, Nadia & Rasheed, Zoya & Ali, Hazrat, 2023. "Light drag in a left-handed atomic medium via Cross Kerr-like nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    12. Kudryashov, Nikolay A., 2020. "Highly dispersive optical solitons of equation with various polynomial nonlinearity law," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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