Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Justification of Peregrine soliton from full water waves   The Peregrine soliton $Q(x,t)=e^{it}(1-\frac{4(1+2it)}{1+4x^2+4t^2})$ is an
exact solution of the 1d focusing nonlinear schr\"{o}dinger equation (NLS)
$iB_t+B_{xx}=-2|B|^2B$, having the feature that it decays to $e^{it}$ at the
spatial and time infinities, and with a peak and troughs in a local region. It
is considered as a prototype of the rogue waves by the ocean waves community.
The 1D NLS is related to the full water wave system in the sense that
asymptotically it is the envelope equation for the full water waves. In this
paper, working in the framework of water waves which decay non-tangentially, we
give a rigorous justification of the NLS from the full water waves equation in
a regime that allows for the Peregrine soliton. As a byproduct, we prove long
time existence of solutions for the full water waves equation with small
initial data in space of the form $H^s(\mathbb{R})+H^{s'}(\mathbb{T})$, where
$s\geq 4, s'>s+\frac{3}{2}$.

27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph