Abstract:
The family of generalized Schrödinger equations is considered with the Kerr
nonlinearity. The partial differential equations are not integrable by the inverse scattering
transform and new solutions of this family are sought taking into account the traveling
wave reduction. The compatibility of the overdetermined system of equations is analyzed and
constraints for parameters of equations are obtained. A modification of the simplest equation
method for finding embedded solitons is presented. A block diagram for finding a solution to
the nonlinear ordinary differential equation is given. The theorem on the existence of bright
solitons for differential equations of any order with Kerr nonlinearity of the family considered
is proved. Exact solutions of embedded solitons described by fourth-, sixth-, eighth and tenth-
order equations are found using the modified algorithm of the simplest equation method. New
solutions for embedded solitons of generalized nonlinear Schrödinger equations with several
extremes are obtained.
This research was supported by the Russian Science Foundation under grant No. 22-11-00141
“Development of Analytical and Numerical Methods for Modeling Waves in Dispersive Wave
Guides”.
Citation:
Nikolay A. Kudryashov, “Embedded Solitons of the Generalized Nonlinear Schrödinger
Equation with High Dispersion”, Regul. Chaotic Dyn., 27:6 (2022), 680–696
\Bibitem{Kud22}
\by Nikolay A. Kudryashov
\paper Embedded Solitons of the Generalized Nonlinear Schrödinger
Equation with High Dispersion
\jour Regul. Chaotic Dyn.
\yr 2022
\vol 27
\issue 6
\pages 680--696
\mathnet{http://mi.mathnet.ru/rcd1187}
\crossref{https://doi.org/10.1134/S1560354722060065}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4519673}
Linking options:
https://www.mathnet.ru/eng/rcd1187
https://www.mathnet.ru/eng/rcd/v27/i6/p680
This publication is cited in the following 9 articles:
Melih Cinar, “Explicit optical solitons of a perturbed Biswas–Milovic equation having parabolic-law nonlinearity and spatio-temporal dispersion”, Opt Quant Electron, 56:5 (2024)
Nikolay A. Kudryashov, Daniil R. Nifontov, “Exact solutions and conservation laws of the fourth-order nonlinear Schrödinger equation for the embedded solitons”, Optik, 303 (2024), 171752
Muslum Ozisik, Aydin Secer, Mustafa Bayram, “Optical soliton solutions of the third-order nonlinear Schrödinger equation in the absence of chromatic dispersion”, Mod. Phys. Lett. B, 2024
Nikolay A. Kudryashov, Daniil R. Nifontov, “Conservation laws and Hamiltonians of the mathematical model with unrestricted dispersion and polynomial nonlinearity”, Chaos, Solitons & Fractals, 175 (2023), 114076
Shafiq Ahmad, Abdul Hameed, Shabir Ahmad, Aman Ullah, Muhammad Akbar, “Stability analysis and some exact solutions of a particular equation from a family of a nonlinear Schrödinger equation with unrestricted dispersion and polynomial nonlinearity”, Opt Quant Electron, 55:8 (2023)
Yakup Y{\i}ld{\i}r{\i}m, Anjan Biswas, Luminita Moraru, Abdulah A. Alghamdi, “Quiescent Optical Solitons for the Concatenation Model with Nonlinear Chromatic Dispersion”, Mathematics, 11:7 (2023), 1709
Anjan Biswas, Jose Vega-Guzman, Yakup Y{\i}ld{\i}r{\i}m, Luminita Moraru, Catalina Iticescu, Abdulah A. Alghamdi, “Optical Solitons for the Concatenation Model with Differential Group Delay: Undetermined Coefficients”, Mathematics, 11:9 (2023), 2012
Elsayed M. E. Zayed, Ahmed H. Arnous, Anjan Biswas, Yakup Y{\i}ld{\i}r{\i}m, Asim Asiri, “Optical solitons for the concatenation model with multiplicative white noise”, J Opt, 2023
Anjan Biswas, Bijan K. Bagchi, Yakup Y{\i}ld{\i}r{\i}m, Salam Khan, Asim Asiri, “Quasimonochromatic dynamical system and optical soliton cooling with triple–power law of self–phase modulation”, Physics Letters A, 480 (2023), 128985
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