Publication Details

This article was originally published as: Marchant, TR, Asymptotic solitons of the extended Korteweg–de Vries equation, Physical Review E, 1999, 59(3), 3745-3748. Copyright 1999 American Physical Society. The original journal can be found here.


The interaction of two higher-order solitary waves, governed by the extended Korteweg–de Vries (KdV) equation, is examined. A nonlocal transformation is used on the extended KdV equation to asymptotically transform it to the KdV equation. The transformation is used to derive the higher-order two-soliton collision and it is found that the interaction is asymptotically elastic. Moreover, the higher-order corrections to the phase shifts suffered by the solitary waves during the collision are found. Comparison is made with a previous result, which indicated that, except for a special case, the interaction of higher-order KdV solitary waves is inelastic, with a coupling, or interaction, term occuring after collision. It is shown that the two theories are asymptotically equivalent, with the coupling term representing the higher-order phase shift corrections. Finally, it is concluded, with the support of existing numerical evidence, that the interpretation of the coupling term as a higher-order phase shift is physically appropriate; hence, the interaction of higher-order solitary waves is asymptotically elastic.



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