Rational solutions to the KdV equation depending on multi-parameters

Pierre Gaillard (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We construct multi-parametric rational solutions to the KdV equation. For this, we use solutions in terms of exponentials depending on several parameters and take a limit when one of these parameters goes to 0. Here we present degenerate rational solutions and give a result without the presence of a limit as a quotient of polynomials depending on 3N parameters. We give the explicit expressions of some of these rational solutions.

Mots clés: KdV equation; rational solutions PACS numbers : 33Q55; 37K10; 47.10A-; 47.35.Fg; 47.54.Bd

Domaines: Physique mathématique [math-ph]

Pierre Gaillard. Rational solutions to the KdV equation depending on multi-parameters. 2021. ⟨hal-03475728⟩