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Stability of solution of Kuramoto-Sivashinsky-Korteweg-de Vries system. (English) Zbl 1154.35441
Summary: A model consisting of a mixed Kuramoto-Sivashinsky-Korteweg-de Vries equation, linearly coupled to an extra linear dissipative equation was proposed in [{\it B. A. Malomed, B.-F. Feng} and {\it T. Kawahara}, Stabilized Kuramoto-Sivashinsky system, Phys. Rev. E 64, 046304 (2001)] in order to describe the surface waves on multilayered liquid films, and stability criteria were discussed using wave mode analysis. In this paper, we study the linear stability of solutions to the model from the viewpoint of the energy estimate.

MSC:
35Q53KdV-like (Korteweg-de Vries) equations
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B25Solitary waves (inviscid fluids)
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References:
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