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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