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
V. A. Shargatov, A. P. Chugainova, A. M. Tomasheva
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引用次数: 0
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.
期刊介绍：
Proceedings of the Steklov Institute of Mathematics is a cover-to-cover translation of the Trudy Matematicheskogo Instituta imeni V.A. Steklova of the Russian Academy of Sciences. Each issue ordinarily contains either one book-length article or a collection of articles pertaining to the same topic.
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