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The third Russian-Chinese conference on complex analysis, algebra, algebraic geometry and mathematical physics
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Stability of stationary solutions of the generalized KdV-Burgers equation A. P. Chugainova Steklov Mathematical Institute of Russian Academy of Sciences, Moscow |
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Abstract: The stability of discontinuities representing solutions of a model generalized KdVÖBurgers equation with a nonmonotone potential is analyzed.The spectral (linear) stability of the structure of special discontinuities was previously studied. Here the spectral stability of nonspecial discontinuities is investigated. The structure of a nonspecial discontinuity represents a phase curve joining two special points: a saddle (the state ahead of the discontinuity) and a focus or node (the state behind the discontinuity). The set of nonspecial discontinuities is examined depending on the dispersion and dissipation parameters. A set of stable nonspecial discontinuities is found. Language: English |
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