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On the Stability of Parametrically Excited Standing Waves

  • Hermann Riecke
Chapter
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Part of the NATO ASI Series book series (NSSB, volume 225)

Abstract

A recent theoretical analysis of parametrically excited standing waves has shown that in systems with large aspect ratio they can exhibit very interesting spatial as well as dynamical behavior1. Under suitable conditions spatially periodic waves were found to be unstable with respect to spatial modulations of the wave number which do not induce the well-known Eckhaus instability. Thus the eventual number of cells in the system does not change, instead the instability leads to the formation of coexisting patches with different wave numbers (“wave-number kinks”). For other parameter values the band of stable wave numbers is found to disappear above a critical value of the external driving. This gives access to a well-controlled transition to a dynamic state which presumably shows chaotic behavior. In the present communication the conditions for the appearance of these two phenomena are discussed in more detail. In particular, the dependence of the phase diffusion coefficient on external as well as internal parameters is presented.

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Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • Hermann Riecke
    • 1
  1. 1.Department of Engineering Sciences and Applied MathematicsNorthwestern UniversityEvanstonUSA

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