Rational solutions to the KPI equation from particular polynomials

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 spatial derivative of a logarithm of a determinant of order n. We obtain 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: Kadomtsev-Petviashvili; Determinants; Polynomials

Domaines: Mathématiques [math]

Pierre Gaillard. Rational solutions to the KPI equation from particular polynomials. Wave Motion, 2022, 108, pp.102828. ⟨10.1016/j.wavemoti.2021.102828⟩. ⟨hal-03537353⟩