Abstract
A generalization of the Korteweg—de Vries equation incorporating an energy input-output balance, hence a dissipation-modified KdV equation is considered. The equation is relevant to describe, for instance, nonlinear Marangoni—Bénard oscillatory instability in a liquid layer heated from above. Cnoidal waves and solitary waves of this equation are obtained both asymptotically and numerically.
Mathematics Subject Classifications (1991): 58F07.
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Rednikov, A.Y., Velarde, M.G., Ryazantsev, Y.S., Nepomnyashchy, A.A., Kurdyumov, V.N. (1995). Cnoidal Wave Trains and Solitary Waves in a Dissipation-Modified Korteweg—de Vries Equation. In: Hazewinkel, M., Capel, H.W., de Jager, E.M. (eds) KdV ’95. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0017-5_26
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DOI: https://doi.org/10.1007/978-94-011-0017-5_26
Publisher Name: Springer, Dordrecht
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