Multi-parameters rational solutions to the mKdV equation

Pierre Gaillard (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

N-order solutions to the modified Korteweg-de Vries (mKdV) equation are given in terms of a quotient of two wronskians of order N depending on 2N real parameters. When one of these parameters goes to 0, we succeed to get for each positive integer N , rational solutions as a quotient of polynomials in x and t depending on 2N real parameters. We construct explicit expressions of these rational solutions for orders N = 1 until N = 6.

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

Domaines: Physique mathématique [math-ph]

Pierre Gaillard. Multi-parameters rational solutions to the mKdV equation. 2021. ⟨hal-03251014⟩