6533b82efe1ef96bd1292f64
RESEARCH PRODUCT
From Fredholm and Wronskian representations to rational solutions to the KPI equation depending on 2N − 2 parameters
Pierre Gaillardsubject
PACS numbers : 33Q55 37K10 4710A- 4735Fg 4754BdRogue WavesWronskians[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]Kadomtsev Petviashvili Equation[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]Fredholm Determinants[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]Lumpsdescription
International audience; 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-05-01 |