Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-similar dynamics for the modified Korteweg-de Vries equation   We prove a local well posedness result for the modified Korteweg-de Vries
equation in a critical space designed so that is contains self-similar
solutions. As a consequence, we can study the flow of this equation around
self-similar solutions: in particular, we give an as-ymptotic description of
small solutions as t $\rightarrow$ +$\infty$ and construct solutions with a
prescribed blow up behavior as t $\rightarrow$ 0.

30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an