Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear damped spatially periodic breathers and the emergence of
  soliton-like rogue waves   The spatially periodic breather solutions (SPBs) of the nonlinear
Schr\"odinger equation, prominent in modeling rogue waves, are unstable. In
this paper we numerically investigate the effects of nonlinear dissipation and
higher order nonlinearities on the routes to stability of the SPBs in the
framework of the nonlinear damped higher order nonlinear Schr\"odinger
(NLD-HONLS) equation. The initial data used in the experiments are generated by
evaluating exact SPB solutions at time $T_0$. The number of instabilities of
the background Stokes wave and the damping strength are varied. The Floquet
spectral theory of the NLS equation is used to interpret and provide a
characterization of the perturbed dynamics in terms of nearby solutions of the
NLS equation. Significantly, as $T_0$ is varied, tiny bands of complex spectrum
are observed to pinch off in the Floquet decomposition of the NLD-HONLS data,
reflecting the breakup of the SPB into a waveform that is close to either a one
or two "soliton-like" structure. For wide ranges of $T_0$, i.e. for solutions
initialized in the early to middle stage of the development of the MI, all
rogue waves are observed to occur when the spectrum is close to a one or two
soliton-like state. When the solutions are initialized as the MI is saturating,
rogue waves also can occur after the spectrum has left a soliton-like state.
Other novel features arise due to nonlinear damping: enhanced asymmetry, two
timescales in the evolution of the spectrum and a delay in the growth of
instabilities due to frequency downshifting.

36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math