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

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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.

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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    A. T. Il’ichev & A. P. Chugainova

Authors
  1. A. T. Il’ichev
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  2. A. P. Chugainova
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Correspondence to A. T. Il’ichev.

Additional information

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Vol. 295, pp. 163–173.

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Il’ichev, A.T., Chugainova, A.P. Spectral stability theory of heteroclinic solutions to the Korteweg-de Vries-Burgers equation with an arbitrary potential. Proc. Steklov Inst. Math. 295, 148–157 (2016). https://doi.org/10.1134/S0081543816080083

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  • DOI: https://doi.org/10.1134/S0081543816080083

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