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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Volume 295, Pages 163–173
DOI: https://doi.org/10.1134/S0371968516040087 (Mi tm3754) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Spectral stability theory of heteroclinic solutions to the Korteweg–de Vries–Burgers equation with an arbitrary potential

A. T. Il'ichev, A. P. Chugainova

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
Full-text PDF (203 kB) Citations (9)
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DOI: https://doi.org/10.1134/S0371968516040087
Abstract: The analysis of stability of heteroclinic solutions to the Korteweg–de Vries–Burgers equation is generalized to the case of an arbitrary potential that gives rise to heteroclinic states. An example of a specific nonconvex potential is given for which there exists a wide set of heteroclinic solutions of different types. Stability of the corresponding solutions in the context of uniqueness of a solution to the problem of decay of an arbitrary discontinuity is discussed.
Funding agency Grant number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.
Received: June 10, 2016
English version:
Proceedings of the Steklov Institute of Mathematics, 2016, Volume 295, Pages 148–157
DOI: https://doi.org/10.1134/S0081543816080083
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: A. T. Il'ichev, A. P. Chugainova, “Spectral stability theory of heteroclinic solutions to the Korteweg–de Vries–Burgers equation with an arbitrary potential”, Modern problems of mechanics, Collected papers, Trudy Mat. Inst. Steklova, 295, MAIK Nauka/Interperiodica, Moscow, 2016, 163–173; Proc. Steklov Inst. Math., 295 (2016), 148–157
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    1. V. A. Shargatov, A. P. Chugainova, A. M. Tomasheva, “Structures of Classical and Special Discontinuities for the Generalized Korteweg–de Vries–Burgers Equation in the Case of a Flux Function with Four Inflection Points”, Proc. Steklov Inst. Math., 322 (2023), 257–272  mathnet  crossref  crossref  mathscinet
    2. A. T. Ilichev, “Ustoichivost granichnykh sostoyanii v beskonechnykh prostranstvennykh oblastyakh”, Lekts. kursy NOTs, 32, MIAN, M., 2022, 3–58  mathnet  crossref
    3. A. P. Chugainova, G. V. Kolomoitsev, V. A. Shargatov, “On the Instability of Monotone Traveling-Wave Solutions for a Generalized Korteweg-–de Vries-–Burgers Equation”, Russ. J. Math. Phys., 29 (2022), 342–357  mathnet  crossref
    4. V. A. Shargatov, A. P. Chugainova, “Stability analysis of traveling wave solutions of a generalized Korteweg-de Vries-Burgers equation with variable dissipation parameter”, J. Comput. Appl. Math., 397 (2021), 113654  crossref  mathscinet  isi
    5. V. A. Shargatov, S. V. Gorkunov, A. T. Il'chev, “Dynamics of front-like water evaporation phase transition interfaces”, Commun. Nonlinear Sci. Numer. Simul., 67 (2019), 223–236  crossref  mathscinet  isi  scopus
    6. A.P. Chugainova, V.A. Shargatov, “Analytical description of the structure of special discontinuities described by a generalized KdV–Burgers equation”, Communications in Nonlinear Science and Numerical Simulation, 66 (2019), 129  crossref
    7. A. G. Kulikovskii, A. P. Chugainova, “Shock waves in anisotropic cylinders”, Proc. Steklov Inst. Math., 300 (2018), 100–113  mathnet  crossref  crossref  mathscinet  isi  elib
    8. V. V. Zharinov, “Hamiltonian operators in differential algebras”, Theoret. and Math. Phys., 193:3 (2017), 1725–1736  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    9. A. P. Chugainova, A. T. Il'ichev, A. G. Kulikovskii, V. A. Shargatov, “Problem of arbitrary discontinuity disintegration for the generalized Hopf equation: selection conditions for a unique solution”, IMA J. Appl. Math., 82:3 (2017), 496–525  crossref  mathscinet  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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