Modulational Stability of Periodic Solutions of the Kuramoto-Sivashinsky Equation.

Abstract

We study the long-wave, modulational, stability of steady periodic solutions of the Kuramoto-Sivashinsky equation. The analysis is fully nonlinear at first, and can in principle be carried out to all orders in the small parameter, which is the ratio of the spatial period to a characteristic length of the envelope perturbations. In the linearized regime we recover a high-order version of the results of Frisch, She and Thual, which shows that the periodic waves are much more stable than previously expected. Modulation theory, Nonlinear stability

Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1993
Accession Number
ADA269128

Entities

People

  • Demetrios T. Papageorgiou
  • George C. Papanicolaou
  • Yiorgos S. Smyrlis

Tags

DTIC Thesaurus Topics

  • Equations
  • Mathematical Analysis
  • Mathematics
  • Modulation
  • Perturbations

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Operations Research