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Tr. Mat. Inst. Steklova, 2016, Volume 295, Pages 163–173 (Mi tm3754)  

This article is cited in 4 scientific papers (total in 4 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

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.


DOI: https://doi.org/10.1134/S0371968516040087

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English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 295, 148–157

Bibliographic databases:

Document Type: Article
UDC: 519.634
Received: June 10, 2016

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, Tr. Mat. Inst. Steklova, 295, MAIK Nauka/Interperiodica, Moscow, 2016, 163–173; Proc. Steklov Inst. Math., 295 (2016), 148–157

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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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