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Preprints, Working Papers, ... Year : 2018

First and second order rational solutions to the Johnson equation and rogue waves

Abstract

Rational solutions to the Johnson equation are constructed as a quotient of two polynomials in x, y and t depending on several real parameters. We obtain an infinite hierarchy of rational solutions written in terms of polynomials of degrees 2N (N + 1) in x, and t, 4N (N + 1) in y, depending on 2N − 2 real parameters for each positive integer N. We construct explicit expressions of the solutions in the cases N = 1 and N = 2 which are given in the following. We study the evolution of the solutions by constructing the patterns of their modulus in the (x, y) plane, and this for different values of parameters.
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Dates and versions

hal-01806297 , version 1 (01-06-2018)

Identifiers

  • HAL Id : hal-01806297 , version 1

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Pierre Gaillard. First and second order rational solutions to the Johnson equation and rogue waves. 2018. ⟨hal-01806297⟩
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