6533b7d7fe1ef96bd1268176
RESEARCH PRODUCT
Fredholm representations of solutions to the KPI equation, their wronkian versions and rogue waves
Pierre Gaillardsubject
Nonlinear Sciences::Exactly Solvable and Integrable Systems[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]Rogue waves[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph][MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]LumpsFredholm determinantsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-06-13 |