From Fredholm and Wronskian representations to rational solutions to the KPI equation depending on 2N − 2 parameters, the structure of the solutions and the case of fourth order
@inproceedings{Gaillard2017FromFA, title={From Fredholm and Wronskian representations to rational solutions to the KPI equation depending on 2N − 2 parameters, the structure of the solutions and the case of fourth order}, author={Pierre Gaillard}, year={2017} }
We have already constructed solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants and wronskians of order 2N. These solutions have been called solutions of order N and they depend on 2N − 1 parameters. We construct here N-order rational solutions. We prove that they can be written as a quotient of 2 polynomials of degree 2N (N + 1) in x, y and t depending on 2N − 2 parameters. We explicitly construct the expressions of the rational solutions of order 4…
3 Citations
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