STRONGLY INTERACTING SOLITARY WAVES FOR THE FRACTIONAL MODIFIED KORTEWEG-DE VRIES EQUATION

Arnaud Eychenne (1) , Frédéric Valet (1)

1 UiB - Department of Mathematics [Bergen]

We study one particular asymptotic behaviour of a solution of the fractional modified Korteweg-de Vries equation (also known as the dispersion generalised modified Benjamin-Ono equation): ∂tu + ∂x(−|D| α u + u 3) = 0. (fmKdV) The dipole solution is a solution behaving in large time as a sum of two strongly interacting solitary waves with different signs. We prove the existence of a dipole for fmKdV. A novelty of this article is the construction of accurate profiles. Moreover, to deal with the non-local operator |D| α , we refine some weighted commutator estimates.

Domaines: Equations aux dérivées partielles [math.AP]

Arnaud Eychenne, Frédéric Valet. STRONGLY INTERACTING SOLITARY WAVES FOR THE FRACTIONAL MODIFIED KORTEWEG-DE VRIES EQUATION. 2022. ⟨hal-03772983⟩