Corrections to the Eckhaus' stability criterion for one-dimensional stationary structures

B. A. Malomed, I. E. Staroselsky, A. B. Konstantinov

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Two amendments to the well-known Eckhaus' stability criterion for small-amplitude non-linear structures generated by weak instability of a spatially uniform state of a non-equilibrium one-dimensional system against small perturbations with finite wavelengths are obtained. Firstly, we evaluate small corrections to the main Eckhaus' term which, on the contrary so that term, do not have a universal form. Comparison of those non-universal corrections with experimental or numerical results gives a possibility to select a more relevant form of an effective nonlinear evolution equation. In particular, the comparison with such results for convective rolls and Taylor vortices gives arguments in favor of the Swift-Hohenberg equation. Secondly, we derive an analog of the Eckhaus criterion for systems degenerate in the sense that in an expansion of their non-linear parts in powers of dynamical variables, the second and third degree terms are absent.

Original languageEnglish
Pages (from-to)270-276
Number of pages7
JournalPhysica D: Nonlinear Phenomena
Issue number1-2
StatePublished - 1989
Externally publishedYes


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