Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Instability of solitons - revisited, I: the critical generalized KdV
  equation   We revisit the phenomenon of instability of solitons in the generalized
Korteweg-de Vries equation, $u_t + \partial_x(u_{xx} + u^p) = 0$. It is known
that solitons are unstable for nonlinearities $p \geq 5$, with the critical
power $p=5$ being the most challenging case to handle. The critical case was
proved by Martel-Merle in [11], where the authors crucially relied on the
pointwise decay estimates of the linear KdV flow. In this paper, we show
simplified approaches to obtain the instability of solitons via truncation and
monotonicity, which can be also useful for other KdV-type equations.

35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys