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Nonautonomous first integrals and general solutions of the KdV-Burgers and mKdV-Burgers equations with the source

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dc.contributor.authorKudryashov, N. A.
dc.contributor.authorSafonova, D. V.
dc.contributor.authorКудряшов, Николай Алексеевич
dc.contributor.authorСафонова, Дарья Владимировна
dc.date.accessioned2024-11-21T09:25:27Z
dc.date.available2024-11-21T09:25:27Z
dc.date.issued2019
dc.description.abstract© 2019 John Wiley & Sons, Ltd.The method for constructing first integrals and general solutions of nonlinear ordinary differential equations is presented. The method is based on index accounting of the Fuchs indices, which appeared during the Painlevé test of a nonlinear differential equation. The Fuchs indices indicate us the leading members of the first integrals for the origin differential equation. Taking into account the values of the Fuchs indices, we can construct the auxiliary equation, which allows to look for the first integrals of nonlinear differential equations. The method is used to obtain the first integrals and general solutions of the KdV-Burgers and the mKdV-Burgers equations with a source. The nonautonomous first integrals in the polynomials form are found. The general solutions of these nonlinear differential equations under at some additional conditions on the parameters of differential equations are also obtained. Illustrations of some solutions of the KdV-Burgers and the mKdV-Burgers are given.
dc.identifier.citationKudryashov, N. A. Nonautonomous first integrals and general solutions of the KdV-Burgers and mKdV-Burgers equations with the source / Kudryashov, N.A., Safonova, D.V. // Mathematical Methods in the Applied Sciences. - 2019. - 10.1002/mma.5684
dc.identifier.doi10.1002/mma.5684
dc.identifier.urihttps://www.doi.org/10.1002/mma.5684
dc.identifier.urihttps://www.scopus.com/record/display.uri?eid=2-s2.0-85066913962&origin=resultslist
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dc.identifier.urihttps://openrepository.mephi.ru/handle/123456789/18217
dc.relation.ispartofMathematical Methods in the Applied Sciences
dc.titleNonautonomous first integrals and general solutions of the KdV-Burgers and mKdV-Burgers equations with the source
dc.typeArticle
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