Families of solutions of order nine to the NLS equation with sixteen parameters

Abstract : We construct new deformations of the Peregrine breather (P9) of order 9 with 16 real parameters. With this method, we obtain explicitly new families of quasi-rational solutions to the NLS equation in terms of a product of an exponential depending on t by a ratio of two polynomials of degree 90 in x and t; when all the parameters are equal to 0, we recover the classical P9 breather. We construct new patterns of different types of rogue waves as triangular configurations of 45 peaks as well as rings and concentric rings.
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Submitted on : Sunday, April 26, 2015 - 4:27:04 PM
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Pierre Gaillard, Mickaël Gastineau. Families of solutions of order nine to the NLS equation with sixteen parameters. 2015. ⟨hal-01145780⟩

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