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# Rational solutions to the KPI equation and multi rogue waves

Abstract : We construct here rational solutions to the Kadomtsev-Petviashvili equation (KPI) as a quotient of two polynomials in $x, y$ and $t$ depending on several real parameters. This method provides an infinite hierarchy of rational solutions written in terms of polynomials of degrees $2N (N + 1)$ in $x, y$ and $t$ depending on $2N - 2$ real parameters for each positive integer $N$. We give explicit expressions of the solutions in the simplest cases $N = 1$ and $N = 2$ and we study the patterns of their modulus in the $(x, y)$ plane for different values of time t and parameters.
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01410308
Contributeur : Imb - Université de Bourgogne <>
Soumis le : mardi 6 décembre 2016 - 15:43:52
Dernière modification le : mardi 10 novembre 2020 - 17:14:04

### Citation

Pierre Gaillard. Rational solutions to the KPI equation and multi rogue waves. Annals of Physics, Elsevier Masson, 2016, 367, pp.1-5. ⟨10.1016/j.aop.2016.01.013⟩. ⟨hal-01410308⟩

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