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Bifurcations of Phase Portraits, Exact Solutions and Conservation Laws of the Generalized Gerdjikov–Ivanov Model

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dc.contributor.authorKudryashov, N. A.
dc.contributor.authorLavrova, S. F.
dc.contributor.authorNifontov, D. R.
dc.contributor.authorКудряшов, Николай Алексеевич
dc.contributor.authorЛаврова, София Федоровна
dc.contributor.authorНифонтов, Даниил Романович
dc.date.accessioned2024-12-27T12:01:34Z
dc.date.available2024-12-27T12:01:34Z
dc.date.issued2023
dc.description.abstractThis article explores the generalized Gerdjikov–Ivanov equation describing the propagation of pulses in optical fiber. The equation studied has a variety of applications, for instance, in photonic crystal fibers. In contrast to the classical Gerdjikov–Ivanov equation, the solution of the Cauchy problem for the studied equation cannot be found by the inverse scattering problem method. In this regard, analytical solutions for the generalized Gerdjikov–Ivanov equation are found using traveling-wave variables. Phase portraits of an ordinary differential equation corresponding to the partial differential equation under consideration are constructed. Three conservation laws for the generalized equation corresponding to power conservation, moment and energy are found by the method of direct transformations. Conservative densities corresponding to optical solitons of the generalized Gerdjikov–Ivanov equation are provided. The conservative quantities obtained have not been presented before in the literature, to the best of our knowledge.
dc.identifier.citationKudryashov, N. A. Bifurcations of Phase Portraits, Exact Solutions and Conservation Laws of the Generalized Gerdjikov–Ivanov Model / Kudryashov, N. A., Lavrova, S. F., Nifontov, D. R. // Mathematics. - 2023. - 11. - № 23. - 10.3390/math11234760
dc.identifier.doi10.3390/math11234760
dc.identifier.urihttps://www.doi.org/10.3390/math11234760
dc.identifier.urihttps://www.scopus.com/record/display.uri?eid=2-s2.0-85178919897&origin=resultslist
dc.identifier.urihttps://openrepository.mephi.ru/handle/123456789/29492
dc.relation.ispartofMathematics
dc.subjectConservation law
dc.subjectPhase portrait
dc.subjectWave Maps Equation
dc.titleBifurcations of Phase Portraits, Exact Solutions and Conservation Laws of the Generalized Gerdjikov–Ivanov Model
dc.typeArticle
dspace.entity.typePublication
oaire.citation.issue23
oaire.citation.volume11
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