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Article Dans Une Revue Journal of Mathematical Physics Année : 2016

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

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Pierre Gaillard
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#### Résumé

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.

### Dates et versions

hal-01414596 , version 1 (12-12-2016)

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• HAL Id : hal-01414596 , version 1
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### Citer

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

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