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Fredholm representations of solutions to the KPI equation, their wronkian versions and 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.
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https://hal.archives-ouvertes.fr/hal-01330610
Contributor : Pierre Gaillard <>
Submitted on : Monday, June 13, 2016 - 7:27:17 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
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  • HAL Id : hal-01330610, version 1

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Pierre Gaillard. Fredholm representations of solutions to the KPI equation, their wronkian versions and rogue waves. 2016. ⟨hal-01330610⟩

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