Particular polynomials generating rational solutions to the KdV equation

Pierre Gaillard (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We construct here rational solutions to the KdV equation by means of particular polynomials. We get solutions in terms of determinants of order n for any positive integer n and we call these solutions, solutions of order n. So we obtain a very efficient method to get rational solutions to the KdV equation and we can construct very easily explicit solutions. In the following, we present some solutions until order 10.

Domaines: Physique mathématique [math-ph]

Pierre Gaillard. Particular polynomials generating rational solutions to the KdV equation. 2022. ⟨hal-03849461⟩