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Asymptotic solitons of the extended Korteweg–de Vries equation

Journal Article


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. © 1999 The American Physical Society.

Publication Date


  • 1999

Citation


  • Marchant, T. R. (1999). Asymptotic solitons of the extended Korteweg–de Vries equation. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 59(3), 3745-3748. doi:10.1103/PhysRevE.59.3745

Scopus Eid


  • 2-s2.0-0012519597

Start Page


  • 3745

End Page


  • 3748

Volume


  • 59

Issue


  • 3

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. © 1999 The American Physical Society.

Publication Date


  • 1999

Citation


  • Marchant, T. R. (1999). Asymptotic solitons of the extended Korteweg–de Vries equation. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 59(3), 3745-3748. doi:10.1103/PhysRevE.59.3745

Scopus Eid


  • 2-s2.0-0012519597

Start Page


  • 3745

End Page


  • 3748

Volume


  • 59

Issue


  • 3