Solitary wave collisions in the regularized long wave equation

H. Kalisch (1) , Marie Hai Yen Nguyen (2) , N.T. Nguyen (1)

1 UiB - University of Bergen
2 LMD - Laboratoire de Météorologie Dynamique (UMR 8539)

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. © 2013 Texas State University - San Marcos.

Domaines: Sciences de la Terre; Physique mathématique [math-ph]

H. Kalisch, Marie Hai Yen Nguyen, N.T. Nguyen. Solitary wave collisions in the regularized long wave equation. Electronic Journal of Differential Equations, 2013, 2013 (19), pp.1-13. ⟨hal-01103539⟩