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On soliton solutions of the Kaup-Kupershmidt equation. II. 'Anomalous' N-soliton solutions

Lookup NU author(s): Dr Allen Parker


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In the second of two articles (designated I [Physica D 137 (2000) 25] and II), exact soliton solutions of the Kaup-Kupershmidt equation are derived using a simplified approach based in part on Hirota's bilinear transform. These solutions have not previously been obtained explicitly by analytic methods. It is found that, at each order, the N-soliton solution is characterised by an additional parameter which accounts for the 'anomalous' nature of these solutions. The first four solitons are constructed explicitly, and in a novel departure from Hirota's method, an iterative procedure is presented for obtaining the general N-soliton solution. Some possible alternative approaches to solving the Kaup-Kupershmidt equation are considered. ©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: 34-48

ISSN (print): 0167-2789

ISSN (electronic): 1872-8022

Publisher: Elsevier BV


DOI: 10.1016/S0167-2789(99)00167-0


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