Stable Periodic Waves in Coupled Kuramoto-Sivashinsky-Korteweg-de Vries Equations

Bao Feng Feng, Boris A. Malomed, Takuji Kawahara

Research output: Contribution to journalArticlepeer-review

Abstract

Periodic waves are investigated in a system composed of a Kuramoto-Sivashinsky-Korteweg-de Vries (KS-KdV) equation linearly coupled to an extra linear dissipative one. The model describes, e.g., a two-layer liquid film flowing down an inclined plane. It has been recently shown that the system supports stable solitary pulses. We demonstrate that a perturbation analysis, based on the balance equation for the net field momentum, predicts the existence of stable cnoidal waves (CnWs) in the same system. It is found that the mean value u0 of the wave field u in the main subsystem, but not the mean value of the extra field, affects the stability of the periodic waves. Three different areas can be distinguished inside the stability region in the parameter plane (L, u0), where L is the wave's period. In these areas, stable are, respectively, CnWs with positive velocity, constant solutions, and CnWs with negative velocity. Multistability, i.e., the coexistence of several attractors, including the waves with several maxima per period, appears at large value of L. The analytical predictions are completely confirmed by direct simulations. Stable waves are also found numerically in the limit of vanishing dispersion, when the KS-KdV equation goes over into the KS one.

Original languageEnglish
Pages (from-to)2700-2707
Number of pages8
JournalJournal of the Physical Society of Japan
Volume71
Issue number11
DOIs
StatePublished - Nov 2002

Keywords

  • Kuramoto-Sivashinsky-Korteweg-de Vries equation
  • Periodic waves

Fingerprint

Dive into the research topics of 'Stable Periodic Waves in Coupled Kuramoto-Sivashinsky-Korteweg-de Vries Equations'. Together they form a unique fingerprint.

Cite this