Description of the inelastic collision of two solitary waves for the BBM equation

TL;DR

This paper analyzes the inelastic collision of two solitary waves in the BBM equation, showing that the collision is nearly elastic with detailed estimates of the residual effects and changes in wave size.

Contribution

It provides a rigorous proof of inelastic but nearly elastic collisions of solitary waves in the BBM equation, with precise residue estimates and collision descriptions.

Findings

Collision is inelastic but almost elastic

Precise estimates of the residual after collision

Description of size change in solitary waves

Abstract

We prove that the collision of two solitary waves of the BBM equation is inelastic but almost elastic in the case where one solitary wave is small in the energy space. We show precise estimates of the nonzero residue due to the collision. Moreover, we give a precise description of the collision phenomenon (change of size of the solitary waves).