Dispersive Stabilization

TL;DR

This paper introduces a method to stabilize ill-posed linear and nonlinear initial value problems by adding nonscalar linear dispersive terms, making them well-posed, with applications to nonlinear optics systems.

Contribution

It presents a novel stabilization technique using dispersive terms, extending the concept of Turing instability to initial value problems.

Findings

Dispersive terms can stabilize ill-posed problems.

Applicable to quasilinear Schrödinger systems in nonlinear optics.

Provides a new perspective on problem stabilization.

Abstract

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 Schr\"odinger equations from nonlinear optics.