Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The genesis of streamwise-localized solutions from globally periodic
  travelling waves in pipe flow   The aim in the dynamical systems approach to transitional turbulence is to
construct a scaffold in phase space for the dynamics using simple invariant
sets (exact solutions) and their stable and unstable manifolds. In large
(realistic) domains where turbulence can co-exist with laminar flow, this
requires identifying exact localized solutions. In wall-bounded shear flows the
first of these has recently been found in pipe flow, but questions remain as to
how they are connected to the many known streamwise-periodic solutions. Here we
demonstrate the origin of the first localized solution in a modulational
symmetry-breaking Hopf bifurcation from a known global travelling wave that has
2-fold rotational symmetry about the pipe axis. Similar behaviour is found for
a global wave of 3-fold rotational symmetry, this time leading to two localized
relative periodic orbits. The clear implication is that all global solutions
should be expected to lead to more realistic localised counterparts through
such bifurcations, which provides a constructive route for their generation.

14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph