Dispersive Stabilization

Guy Metivier (1) , Jeffrey Rauch (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 Department of Mathematics - University of Michigan

Ill posed linear and nonlinear initial value problems may be stabilized, that it converted to to well posed initial value problems, by the addition of purely nonscalar linear dispersive terms. This is a stability analog of the Turing instability. This idea applies to systems of quasilinear Schrödinger equations from nonlinear optics.

Mots clés: Systems of Shrödinger equations; nonlinear symbolic calculus

Domaines: Equations aux dérivées partielles [math.AP]

Guy Metivier, Jeffrey Rauch. Dispersive Stabilization. Bull. London Math Soc, 2010, 42, pp.250--262. ⟨hal-00367785⟩