Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear envelope equation and nonlinear Landau damping rate for a
  driven electron plasma wave   In this paper, we provide a theoretical description, and calculate, the
nonlinear frequency shift, group velocity and collionless damping rate, $\nu$,
of a driven electron plasma wave (EPW). All these quantities, whose physical
content will be discussed, are identified as terms of an envelope equation
allowing one to predict how efficiently an EPW may be externally driven. This
envelope equation is derived directly from Gauss law and from the investigation
of the nonlinear electron motion, provided that the time and space rates of
variation of the EPW amplitude, $E_p$, are small compared to the plasma
frequency or the inverse of the Debye length. $\nu$ arises within the EPW
envelope equation as more complicated an operator than a plain damping rate,
and may only be viewed as such because $(\nu E_p)/E_p$ remains nearly constant
before abruptly dropping to zero. We provide a practical analytic formula for
$\nu$ and show, without resorting to complex contour deformation, that in the
limit $E_p \to 0$, $\nu$ is nothing but the Landau damping rate. We then term
$\nu$ the "nonlinear Landau damping rate" of the driven plasma wave. As for the
nonlinear frequency shift of the EPW, it is also derived theoretically and
found to assume values significantly different from previously published ones,
assuming that the wave is freely propagating. Moreover, we find no limitation
in $k \lambda_D$, $k$ being the plasma wavenumber and $\lambda_D$ the Debye
length, for a solution to the dispertion relation to exist, and want to stress
here the importance of specifying how an EPW is generated to discuss its
properties. Our theoretical predictions are in excellent agreement with results
inferred from Vlasov simulations of stimulated Raman scattering (SRS), and an
application of our theory to the study of SRS is presented.

26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math