Moving breathers and breather-to-soliton conversions for the Hirota equation

We find that the Hirota equation admits breather-to-soliton conversion at special values of the solution eigenvalues. This occurs for the first-order, as well as higher orders, of breather solutions. An analytic expression for the condition of the transformation is given and several examples of tran...

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Bibliographic Details
Published in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2015-08, Vol.471 (2180), p.20150130
Main Authors: Chowdury, A., Ankiewicz, A., Akhmediev, N.
Format: Article
Language:English
Subjects:
Breather-Soliton Dynamics
Darboux Transformation
Hirota Equation
Nonlinear Schrödinger Equation
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Summary:We find that the Hirota equation admits breather-to-soliton conversion at special values of the solution eigenvalues. This occurs for the first-order, as well as higher orders, of breather solutions. An analytic expression for the condition of the transformation is given and several examples of transformations are presented. The values of these special eigenvalues depend on two free parameters that are present in the Hirota equation. We also find that higher order breathers generally have complicated quasi-periodic oscillations along the direction of propagation. Various breather solutions are considered, including the particular case of second-order breathers of the nonlinear Schrödinger equation.
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.2015.0130