On traveling-wave solutions of the Kuramoto-Sivashinsky equation

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23 引文 斯高帕斯(Scopus)

摘要

Previous numerical results indicate that the Kuramoto-Sivashinsky equation admits three classes of non-periodic traveling-wave solutions, namely regular shocks, oscillatory shocks, and solitary waves. However, it has been shown that regular (monotonic) shocks cease to exist in the weak-shock limit, due to the radiation of oscillatory waves of exponentially small (with respect to the shock strength) but growing (in space) amplitude. Here, oscillatory shocks and solitary waves are constructed by asymptotic analysis. It thus transpires that, in the weak-shock limit, oscillatory shocks can only be antisymmetric, otherwise oscillatory and monotonic waves of exponentially small but growing (in space) amplitude would inevitably be excited. Under certain conditions, however, the growing waves can link a nearly antisymmetric oscillatory shock with a radiating regular shock to form a solitary wave. The predictions of the asymptotic theory are supported by numerical results.

原文English
頁(從 - 到)25-42
頁數18
期刊Physica D: Nonlinear Phenomena
110
發行號1-2
DOIs
出版狀態Published - 1997

All Science Journal Classification (ASJC) codes

  • 統計與非線性物理學
  • 數學物理學
  • 凝聚態物理學
  • 應用數學

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