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Shock waves in the modified Korteweg-de Vries-Burgers equation

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Summary

The asymptotics ast → + ∞ of shock waves of the modified Korteweg-de Vries-Burgers (MKdV-B) equation is investigated. An attractor interpretation of shock problems for integrable systems is presented and some problems of nonlinear stability are discussed. The MKdV-B equation is considered as a nonconservative perturbation of the integrable modified Korteweg-de Vries (MKdV) equation. The MKdV equation considered here has anon-self-adjoint Lax pair. In spite of this difficulty, acomplex Whitham deformation is constructed.

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  1. St. Petersburg Branch of The Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, 191011, St. Petersburg, Russia

    R. F. Bikbaev

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Communicated by Thanasis Fokas

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Bikbaev, R.F. Shock waves in the modified Korteweg-de Vries-Burgers equation. J Nonlinear Sci 5, 1–10 (1995). https://doi.org/10.1007/BF01869099

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