• Corpus ID: 42543256

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}
}

• P. Gaillard
• Published 1 May 2017
• Mathematics

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 depending on 6 real parameters and we study the patterns of their modulus in the plane (x, y) and their evolution according to time and parameters a1, a2, a3, b1, b2, b3.