TY - JOUR
T1 - Corrections to the Eckhaus' stability criterion for one-dimensional stationary structures
AU - Malomed, B. A.
AU - Staroselsky, I. E.
AU - Konstantinov, A. B.
PY - 1989
Y1 - 1989
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0347167711&partnerID=8YFLogxK
U2 - 10.1016/0167-2789(89)90239-X
DO - 10.1016/0167-2789(89)90239-X
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AN - SCOPUS:0347167711
SN - 0167-2789
VL - 34
SP - 270
EP - 276
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 1-2
ER -