Localized coherent structures of (2+1) dimensional generalizations of soliton systems |
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Authors: | M Lakshmanan R Radha |
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Institution: | (1) Centre for Nonlinear Dynamics, Department of Physics, Bharathidasan University, 620 024 Tiruchirapalli, India |
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Abstract: | 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 Painlevé 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. |
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Keywords: | Solitons in higher dimensions integrability coherent structures Painlevé analysis Hirota method |
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