Deformations of higher order Peregrine breathers and monstrous polynomials.

Abstract : In the following, we present two new results about the focusing one dimensional NLS equation : 1. We construct solutions of NLS equation in terms of wronskians. Then performing a special passage to the limit when a parameter tends to 0, we obtain quasi-rational solutions of NLS equation. 2. We construct quasi-rational solutions in terms of determinants without of a limit. Which is new is that we obtain at order N, solutions depending on 2N-2 parameters. 3. When all these parameters are equal to zeros, we recover Peregrine breathers; it is the reason why we call these solutions deformations of Peregrine breathers. \\ Then we deduce new patterns of solutions in the (x,t) plane for the orders N=3 to N=10.
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Conference papers
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https://hal.archives-ouvertes.fr/hal-00833406
Contributor : Pierre Gaillard <>
Submitted on : Wednesday, June 12, 2013 - 4:04:24 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM

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  • HAL Id : hal-00833406, version 1

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Pierre Gaillard. Deformations of higher order Peregrine breathers and monstrous polynomials.. Deformations of higher order Peregrine breathers and monstrous polynomials., Jun 2013, PEKIN, China. ⟨hal-00833406⟩

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