Interfacial waves with free-surface boundary conditions: An approach via a model equation.

*(English)*Zbl 1037.76010From the summary: The title interfacial-wave problem is reduced to a system of ordinary differential equations by using a classical perturbation method, which takes into consideration the possible resonance between short waves and “slow” solitary waves. In the past, classical Korteweg-de Vries type models have been derived but cannot deal with the resonance. All solutions of the new system of model equations, including classical as well as generalized solitary waves, are constructed. The domain of validity of the model is discussed as well. It is also shown that fronts connecting two conjugate states cannot occur for “fast” waves. For “slow” waves, fronts exist but they have ripples in their tails.

##### MSC:

76B55 | Internal waves for incompressible inviscid fluids |

76B25 | Solitary waves for incompressible inviscid fluids |

35Q51 | Soliton equations |

##### Keywords:

two-fluid system; fast waves; slow waves; perturbation method; resonance; generalized solitary waves
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\textit{F. Dias} and \textit{A. Il'ichev}, Physica D 150, No. 3--4, 278--300 (2001; Zbl 1037.76010)

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