Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two remarks on the generalised Korteweg de-Vries equation   We make two observations concerning the generalised Korteweg de Vries
equation $u_t + u_{xxx} = \mu (|u|^{p-1} u)_x$. Firstly we give a scaling
argument that shows, roughly speaking, that any quantitative scattering result
for $L^2$-critical equation ($p=5$) automatically implies an analogous
scattering result for the $L^2$-critical nonlinear Schr\"odinger equation $iu_t
+ u_{xx} = \mu |u|^4 u$. Secondly, in the defocusing case $\mu > 0$ we present
a new dispersion estimate which asserts, roughly speaking, that energy moves to
the left faster than the mass, and hence strongly localised soliton-like
behaviour at a fixed scale cannot persist for arbitrarily long times.

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The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat