Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical Continuation of Invariant Solutions of the Complex
  Ginzburg-Landau Equation   We consider the problem of computation and deformation of group orbits of
solutions of the complex Ginzburg-Landau equation (CGLE) with cubic
nonlinearity in $1\!+\!1$ space-time dimension invariant under the action of
the three-dimensional Lie group of symmetries $A(x,t) \rightarrow
\mathrm{e}^{\mathrm{i}\theta}A(x+\sigma,t+\tau)$. From an initial set of group
orbits of invariant solutions, for a particular point in the parameter space of
the CGLE, we obtain new sets of group orbits of invariant solutions via
numerical continuation along paths in the moduli space. The computed solutions
along the continuation paths are unstable, and have multiple modes and
frequencies active in their spatial and temporal spectra, respectively.
Structural changes in the moduli space resulting in symmetry gaining / breaking
associated often with the spatial reflection symmetry $A(x,t) \rightarrow
A(-x,t)$ of the CGLE were frequently uncovered in the parameter regions
traversed.

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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th