Localized coherent structures of (2+1) dimensional generalizations of soliton systems

Lakshmanan, M. ; Radha, R. (1997) Localized coherent structures of (2+1) dimensional generalizations of soliton systems Pramana - Journal of Physics, 48 (1). pp. 163-188. ISSN 0304-4289

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Official URL: http://www.ias.ac.in/j_archive/pramana/48/1-2/163-...

Related URL: http://dx.doi.org/10.1007/BF02845629


We briefly review the recent progress in obtaining (2+1) dimensional integrable generalizations of soliton equations in (1+1) dimensions. Then, we develop an algorithmic procedure to obtain interesting classes of solutions to these systems. In particular using a Painleve singularity structure analysis approach, we investigate their integrability properties and obtain their appropriate Hirota bilinearized forms. We identify line solitons and from which we introduce the concept of ghost solitons, which are patently boundary effects characteristic of these (2+1) dimensional integrable systems. Generalizing these solutions, we obtain exponentially localized solutions, namely the dromions which are driven by the boundaries. We also point out the interesting possibility that while the physical field itself may not be localized, either the potential or composite fields may get localized. Finally, the possibility of generating an even wider class of localized solutions is hinted by using curved solitons.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Solitons in Higher Dimensions; Integrability; Coherent Structures; Painleve Analysis; Hirota Method
ID Code:19653
Deposited On:22 Nov 2010 12:09
Last Modified:17 May 2016 04:09

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