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Regular and Chaotic Dynamics, 2022, Volume 27, Issue 6, Pages 680–696
DOI: https://doi.org/10.1134/S1560354722060065
(Mi rcd1187)
 

This article is cited in 9 scientific papers (total in 9 papers)

Alexey Borisov Memorial Volume

Embedded Solitons of the Generalized Nonlinear Schrödinger Equation with High Dispersion

Nikolay A. Kudryashov

Department of Applied Mathematics, National Research Nuclear University MEPHI, Kashirskoe sh. 31, 115409 Moscow, Russia
Citations (9)
References:
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.
Keywords: generalized Schrödinger equation, optical soliton, embedded soliton, simplest equa- tion method, exact solution.
Funding agency Grant number
Russian Science Foundation 22-11-00141
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”.
Received: 23.08.2022
Accepted: 13.10.2022
Bibliographic databases:
Document Type: Article
MSC: 34M55
Language: English
Citation: Nikolay A. Kudryashov, “Embedded Solitons of the Generalized Nonlinear Schrödinger Equation with High Dispersion”, Regul. Chaotic Dyn., 27:6 (2022), 680–696
Citation in format AMSBIB
\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}
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  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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