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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

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Abstract

We study the structure of the set of traveling wave solutions for the generalized Korteweg–de Vries–Burgers equation with the flux function having four inflection points. In this case there arise two monotone structures of stable special discontinuities propagating at different velocities (such a situation has not been described earlier in the literature). Both structures of special discontinuities are linearly stable. To analyze the linear stability of the structures of classical and special discontinuities, we apply a method based on the use of the Evans function. We also propose a conjecture that establishes the admissibility of classical discontinuities in the case when there are two stable special discontinuities.

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Funding

This work is supported by the Russian Foundation for Basic Research, project no. 20-01-00071.

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Authors and Affiliations

  1. National Research Nuclear University MEPhI, Kashirskoe sh. 31, Moscow, 115409, Russia

    V. A. Shargatov & A. M. Tomasheva

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

    A. P. Chugainova

Authors
  1. V. A. Shargatov
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  2. A. P. Chugainova
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  3. A. M. Tomasheva
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Correspondence to V. A. Shargatov or A. P. Chugainova.

Additional information

Translated from Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2023, Vol. 322, pp. 266–281 https://doi.org/10.4213/tm4314.

Translated by K. Shubik

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Shargatov, V.A., Chugainova, A.P. & Tomasheva, A.M. 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, 257–272 (2023). https://doi.org/10.1134/S0081543823040211

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  • DOI: https://doi.org/10.1134/S0081543823040211

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