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