The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 24, Number 2 (2014), 616-651.
Stability of solitons under rapidly oscillating random perturbations of the initial conditions
We use the inverse scattering transform and a diffusion approximation limit theorem to study the stability of soliton components of the solution of the nonlinear Schrödinger and Korteweg–de Vries equations under random perturbations of the initial conditions: for a wide class of rapidly oscillating random perturbations this problem reduces to the study of a canonical system of stochastic differential equations which depends only on the integrated covariance of the perturbation. We finally study the problem when the perturbation is weak, which allows us to analyze the stability of solitons quantitatively.
Ann. Appl. Probab., Volume 24, Number 2 (2014), 616-651.
First available in Project Euclid: 10 March 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60B12: Limit theorems for vector-valued random variables (infinite- dimensional case) 35C08: Soliton solutions
Secondary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Fedrizzi, Ennio. Stability of solitons under rapidly oscillating random perturbations of the initial conditions. Ann. Appl. Probab. 24 (2014), no. 2, 616--651. doi:10.1214/13-AAP931. https://projecteuclid.org/euclid.aoap/1394465367