Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 19, pp. 1-13.

Title: Solitary wave collisions in the regularized long wave equation
        
Authors: Henrik Kalisch   (Univ. of Bergen, Norway)
         Marie Hai Yen Nguyen (Univ. Paris 6, Cedex 05, France)
         Nguyet Thanh Nguyen  (Univ. of Bergen, Norway)
        
Abstract:
 The regularized long-wave equation admits families of positive and
 negative solitary waves. Interactions of these waves are studied,
 and it is found that interactions of pairs of positive and pairs of
 negative solitary waves feature the same phase shift asymptotically
 as the wave velocities grow large as long as the same amplitude ratio is
 maintained. The collision of a positive with a negative wave leads to a
 host of phenomena, including resonance, annihilation and creation of
 secondary waves. A sharp criterion on the resonance for positive-negative
 interactions is found.

Submitted November 26, 2012. Published January 23, 2013.
Math Subject Classifications: 35Q53, 35B34, 35C08.
Key Words: Solitary waves; solitary-wave interaction; phase shift; resonance