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Funktsional'nyi Analiz i ego Prilozheniya, 2009, Volume 43, Issue 4, Pages 87–90
DOI: https://doi.org/10.4213/faa2954 (Mi faa2954) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Brief communications

Three Series of Invariant Manifolds of the Sawada–Kotera Equation

Yu. Yu. Bagderina

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
Full-text PDF (130 kB) Citations (5)
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DOI: https://doi.org/10.4213/faa2954
Abstract: We find a new infinite sequence of invariant manifolds for the Sawada–Kotera equation, in addition to the known two sequences of its symmetries and conservation laws. The elements of these three sequences are related cyclically by recursion relations similar to the Lenard formula for the KdV equation. For any n>0, there are two invariant manifolds of order 2n, which allows one to construct two n-soliton solutions of the Sawada–Kotera equation.
Keywords: evolution equation, invariant manifold, symmetry, conservation law, soliton solution.
Received: 14.03.2008
English version:
Functional Analysis and Its Applications, 2009, Volume 43, Issue 4, Pages 312–315
DOI: https://doi.org/10.1007/s10688-009-0038-6
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: Yu. Yu. Bagderina, “Three Series of Invariant Manifolds of the Sawada–Kotera Equation”, Funktsional. Anal. i Prilozhen., 43:4 (2009), 87–90; Funct. Anal. Appl., 43:4 (2009), 312–315
Citation in format AMSBIB
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\jour Funktsional. Anal. i Prilozhen.
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\pages 87--90
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\transl
\jour Funct. Anal. Appl.
\yr 2009
\vol 43
\issue 4
\pages 312--315
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  • https://www.mathnet.ru/eng/faa2954
  • https://doi.org/10.4213/faa2954
  • https://www.mathnet.ru/eng/faa/v43/i4/p87
    • This publication is cited in the following 5 articles:
    1. Zhong Wang, “Spectral stability of multi-solitons for generalized Hamiltonian system I: The Caudrey–Dodd–Gibbon–Sawada–Kotera equation”, Physica D: Nonlinear Phenomena, 444 (2023), 133610  crossref
    2. A. V. Domrin, M. A. Shumkin, B. I. Suleimanov, “Meromorphy of solutions for a wide class of ordinary differential equations of Painlevé type”, Journal of Mathematical Physics, 63:2 (2022)  crossref
    3. Li Yu., Chen Y., “The Special Class of Second Integrals of the Kdv Equation”, Commun. Nonlinear Sci. Numer. Simul., 70 (2019), 193–202  crossref  mathscinet  isi
    4. Kunzinger M., Popovych R.O., “Generalized conditional symmetries of evolution equations”, J. Math. Anal. Appl., 379:1 (2011), 444–460  crossref  mathscinet  zmath  isi  elib  scopus
    5. Bagderina Yu.Yu., “Invariants of a family of third-order ordinary differential equations”, J. Phys. A, 42:8 (2009), 085204, 21 pp.  crossref  mathscinet  zmath  adsnasa  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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