Abstract

A head-on collision between two solitary waves from opposite directions in a Rayleigh-B\'enard convecting fluid is investigated by use of the Poincar\'e-Lighthill-Kuo method. The fluid system is bounded below by an isothermic plane and above a free deformable surface on which a heat flux is fixed. The results show that, near the transition of the long-wavelength oscillatory instability, the solitary waves emerging from the collision can preserve their original identities to the second order. The phase shifts due to the collision are calculated explicitly.

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