From particular polynomials to rational solutions to the KPI equation

Pierre Gaillard (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We construct solutions to the Kadomtsev-Petviashvili equation (KPI) from particular polynomials. We obtain rational solutions written as a second derivative with respect to the variable x of a logarithm of a determinant of order n. So we get with this method an infinite hierarchy of rational solutions to the KPI equation. We give explicitly the expressions of these solutions for the first five orders.

Mots clés: numbers : 33Q55; 37K10; 47.10A-; 47.35.Fg; 47.54.Bd

Domaines: Physique mathématique [math-ph]

Pierre Gaillard. From particular polynomials to rational solutions to the KPI equation. 2022. ⟨hal-03725302⟩