Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic stability of solitons to 1D Nonlinear Schrodinger Equations
  in subcritical case   In this paper, we prove the asymptotic stability of solitary waves to 1D
nonlinear Schr\"odinger equations in the subcritical case with symmetry and
spectrum assumptions. One of the main ideas is to use the vector fields method
developed by Cuccagna, Georgiev, Visciglia to overcome the weak decay with
respect to $t$ of the linearized equation caused by the one dimension setting
and the weak nonlinearity caused by the subcritical growth of the nonlinearity
term. Meanwhile, we apply the polynomial growth of the high Sobolev norms of
solutions to 1D Schr\"odinger equations obtained by Staffilani to control the
high moments of the solutions emerging from the vector fields method.

22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci