Asymptotic solitons of the extended Korteweg–de Vries equation

T. R. Marchant
Phys. Rev. E 59, 3745 – Published 1 March 1999
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Abstract

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.

  • Received 12 August 1998

DOI:https://doi.org/10.1103/PhysRevE.59.3745

©1999 American Physical Society

Authors & Affiliations

T. R. Marchant

  • School of Mathematics and Applied Statistics, University of Wollongong, Wollongong 2522, New South Wales, Australia

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Vol. 59, Iss. 3 — March 1999

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