From finite-gap solutions of KdV in terms of theta functions to solitons and positons

Pierre Gaillard (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We degenerate the finite gap solutions of the KdV equation from the general formulation in terms of abelian functions when the gaps tends to points, to recover solutions of KdV equations in terms of wronskians called solitons or positons. For this we establish a link between Fredholm determinants and Wronskians.

Mots clés: KdV; Riemann surfaces:; theta functions; solitons; positons

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Pierre Gaillard. From finite-gap solutions of KdV in terms of theta functions to solitons and positons. 2010. ⟨hal-00466159v2⟩