Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability Analysis of the Lugiato-Lefever Model for Kerr Optical
  Frequency Combs. Part II: Case of Anomalous Dispersion   We present a stability analysis of the Lugiato-Lefever model for Kerr optical
frequency combs in whispering gallery mode resonators pumped in the anomalous
dispersion regime. This article is the second part of a research work whose
first part was devoted to the regime of normal dispersion, and was presented in
ref. \cite{Part_I}. The case of anomalous dispersion is indeed the most
interesting from the theoretical point of view, because of the considerable
variety of dynamical behaviors that can be observed. From a technological point
of view, it is also the most relevant because it corresponds to the regime
where Kerr combs are predominantly generated, studied, and used for different
applications. In this article, we analyze the connection between the spatial
patterns and the bifurcation structure of the eigenvalues associated to the
various equilibria of the system. The bifurcation map evidences a considerable
richness from a dynamical standpoint. We study in detail the emergence of
super- and sub-critical Turing patterns in the system. We determine the areas
were bright isolated cavity solitons emerge, and we show that soliton molecules
can emerge as well. Very complex temporal patterns can actually be observed in
the system, where solitons (or soliton complexes) co-exist with or without
mutual interactions. Our investigations also unveil the mechanism leading to
the phenomenon of breathing solitons. Two routes to chaos in the system are
identified, namely a route via the so called secondary combs, and another via
soliton breathers. The Kerr combs corresponding to all these temporal patterns
are analyzed in detail, and a discussion is led about the possibility to gain
synthetic comprehension of the observed spectra out of the dynamical complexity
of the system.

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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga