Localized coherent structures of Ishimori equation I through Hirota's bilinearization method: time dependent/stationary boundaries

Vijayalakshmi, S. ; Lakshmanan, M. (2007) Localized coherent structures of Ishimori equation I through Hirota's bilinearization method: time dependent/stationary boundaries Chaos, Solitons & Fractals, 33 (1). pp. 203-216. ISSN 0960-0779

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S09600...

Related URL: http://dx.doi.org/10.1016/j.chaos.2006.01.032

Abstract

Ishimori equation is a (2 + 1) dimensional generalization of the (1 + 1) dimensional integrable classical continuous Heisenberg ferromagnetic spin equation. The richness of the coherent structures admitted by Ishimori equation I such as dromion, lump and rationally-exponentially localized solutions, have been demonstrated in the literature through ∂- technique and binary Darboux transformation method. To our knowledge Hirota's method had been adopted to construct only the vortex solutions of Ishimori equation II. For the first time, the various types of localized coherent structures mentioned above have been constructed in this paper for the Ishimori equation I using the Hirota's direct method. In particular we have brought out the significance of boundaries and arbitrary functions in generating all these types of localized structures and proved that the absence of such boundaries leads only to line soliton solutions.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
ID Code:19631
Deposited On:22 Nov 2010 12:16
Last Modified:17 May 2016 04:08

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