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On soliton solutions of the Kaup-Kupershmidt equation. I. Direct bilinearisation and solitary wave

Lookup NU author(s): Dr Allen Parker


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In this first of two papers (designated I and II [Physica D 137 (2000) 34]), a direct procedure is given for bilinearising the Kaup-Kupershmidt and Sawada-Kotera equations. It is found that, whereas the Sawada-Kotera equation can be written in bilinear form in two distinct ways (which are shown to be equivalent), the Kaup-Kupershmidt equation has a single bilinear representation. This distinguishing feature, which has previously received no explanation, has consequences for obtaining the soliton solutions of these two closely related fifth-order integrable equations. The 'anomalous' solitary wave of the Kaup-Kupershmidt equation is reconstructed, and a simplified approach to obtaining its N-soliton solutions is proposed. This provides the basis for constructing these solutions explicitly in II. © 2000 Elsevier Science B.V. All rights reserved.

Publication metadata

Author(s): Parker A

Publication type: Article

Publication status: Published

Journal: Physica D: Nonlinear Phenomena

Year: 2000

Volume: 137

Issue: 1-2

Pages: 25-33

ISSN (print): 0167-2789

ISSN (electronic): 1872-8022

Publisher: Elsevier BV


DOI: 10.1016/S0167-2789(99)00166-9


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