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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Article dans une revue
Journal of Mathematical Physics, American Institute of Physics (AIP), 2016, 57 (6), pp.063505. <http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4953383>. <10.1063/1.4953383>
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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 : mardi 13 décembre 2016 - 09:30:19

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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), pp.063505. <http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4953383>. <10.1063/1.4953383>. <hal-01414596>

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