Rational solutions of order N to the KPI equation with multi-parameters and the explicit case of order 3

P Gaillard (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We present multiparametric rational solutions to the Kadomtsev-Petviashvili equation (KPI). These solutions of order N depend on 2N − 2 real parameters. Explicit expressions of the solutions at order 3 are given. They can be expressed as a quotient of a polynomial of degree 2N (N + 1) − 2 in x, y and t by a polynomial of degree 2N (N + 1) in x, y and t, depending on 2N − 2 real parameters. We study the patterns of their modulus in the (x,y) plane for different values of time t and parameters.

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

Domaines: Physique mathématique [math-ph]

P Gaillard. Rational solutions of order N to the KPI equation with multi-parameters and the explicit case of order 3. 2022. ⟨hal-03688578⟩