Henrik Kalisch, Marie Hai Yen Nguyen, Nguyet Thanh Nguyen
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
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Henrik Kalisch Department of Mathematics, University of Bergen Postbox 7800, 5020 Bergen, Norway email: henrik.kalisch@math.uib.no |
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Marie Hai Yen Nguyen Laboratoire de météorologie dynamique Université Paris 6, 75252 Paris Cedex 05, France email:mathsyen@yahoo.com |
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Nguyet Thanh Nguyen Department of Mathematics, University of Bergen Postbox 7800, 5020 Bergen, Norway email: nguyen.nguyet13@yahoo.com |
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