Inelastic interaction of nearly equal solitons for the BBM equation

Yvan Martel; Frank Merle

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arXiv · 0911.0932

Inelastic interaction of nearly equal solitons for the BBM equation

Yvan Martel·Frank Merle

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Abstract

This paper is concerned with the interaction of two solitons of nearly equal speeds for the (BBM) equation. This work is an extension of the results obtained in arXiv:0910.3204 by the same authors, addressing the same question for the quartic (gKdV) equation. First, we prove that the two solitons are preserved by the interaction and that for all time they are separated by a large distance, as in the case of the integrable (KdV) equation in this regime. Second, we prove that the collision is not perfectly elastic, except in the integrable case (i.e. in the limiting case of the (KdV) equation).

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Yvan Martel, Frank Merle. 2009-11-04. Inelastic interaction of nearly equal solitons for the BBM equation. https://arxiv.org/abs/0911.0932

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