Degenerate determinant representation of solutions of the NLS equation, higher Peregrine breathers and multi-rogue waves.

Abstract : We present a new representation of solutions of the focusing NLS equation as a quotient of two determinants. This work is based on a recent paper in which we have constructed a multi-parametric family of this equation in terms of wronskians. This formulation was written in terms of a limit involving a parameter. Here we give a very compact formulation without presence of a limit. This is a completely new result which gives a very efficient procedure to construct families of quasi-rational solutions of the NLS equation. With this method, we construct Peregrine breathers of orders N=4 to 7 and multi-rogue waves associated by deformation of parameters.
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Submitted on : Sunday, September 16, 2012 - 11:23:13 AM
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  • HAL Id : hal-00650528, version 3

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Pierre Gaillard. Degenerate determinant representation of solutions of the NLS equation, higher Peregrine breathers and multi-rogue waves.. 2012. ⟨hal-00650528v3⟩

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