Stability of solitons under rapidly oscillating random perturbations of the initial conditions

DOI10.1214/13-AAP931zbMath1315.35053arXiv1201.3753MaRDI QIDQ2448690

Ennio Fedrizzi

Publication date: 5 May 2014

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.3753

zbMATH Keywords

inverse scattering transformsolitonsKdV equationNLS equationcompletely integrable systemsdiffusion approximation limit theoremrandom perturbation of initial conditions

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs with randomness, stochastic partial differential equations (35R60) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12) Soliton solutions (35C08)

Cites Work

• Convergence faible et principe d'invariance pour des martingales à valeurs dans des espaces de Sobolev
• Solutions of the Korteweg-de Vries equation from irregular data
• Stopping times and tightness
• Wave propagation and time reversal in randomly layered media.
• The soliton number of optical soliton bound states for two special families of input pulses
• Soliton Evolution in the Presence of Perturbation
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