# Fredholm and Wronskian representations of solutions to the KPI equation and multi-rogue waves

Abstract : We construct solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants. We deduce solutions written as a quotient of Wronskians of order $2N$. These solutions, called solutions of order $N$, depend on $2N - 1$ parameters. When one of these parameters tends to zero, we obtain $N$ order rational solutions expressed as a quotient of two polynomials of degree $2N( N + 1)$ in $x, y,$ and $t$ depending on $2N - 2$ parameters. So we get with this method an infinite hierarchy of solutions to the KPI equation. Published by AIP Publishing.
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Type de document :
Article dans une revue
Journal of Mathematical Physics, American Institute of Physics (AIP), 2016, 57 (6), 〈10.1063/1.4953383〉
Domaine :
Liste complète des métadonnées

https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01414596
Contributeur : Imb - Université de Bourgogne <>
Soumis le : lundi 12 décembre 2016 - 14:26:33
Dernière modification le : mercredi 28 mars 2018 - 07:22:57

### Citation

Pierre Gaillard. Fredholm and Wronskian representations of solutions to the KPI equation and multi-rogue waves. Journal of Mathematical Physics, American Institute of Physics (AIP), 2016, 57 (6), 〈10.1063/1.4953383〉. 〈hal-01414596〉

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