Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Order Parameter for the Transition from Phase to Amplitude Turbulence   The maximal conserved phase gradient is introduced as an order parameter to
characterize the transition from phase- to defect-turbulence in the complex
Ginzburg-Landau equation. It has a finite value in the phase-turbulent regime
and decreases to zero when the transition to defect-turbulence is approached.
Solutions with a non-zero phase gradient are studied via a Lyapunov analysis.
The degree of "chaoticity" decreases for increasing values of the phase
gradient and finally leads to stable travelling wave solutions. A modified
Kuramoto-Sivashinsky equation for the phase-dynamics is able to reproduce the
main features of the stable waves and to explain their origin.

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The categories of this paper are: physics
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The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
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The categories of this paper are: econ
31
The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: eess