Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient determination of the energy landscape of nonlinear
  Schr\"odinger-type equations   We describe a systematic approach for the efficient numerical solution of
nonlinear Schr\"odinger-type partial differential equations of the form $(K +V
+ g|\psi|^2)\psi=0$, with an energy operator $K$, a scalar potential $V$, and a
scalar parameter $g$. Instrumental to the approach are developments in
numerical linear and nonlinear algebra, specifically numerical parameter
continuation. We demonstrate how a continuous sequence of solutions can be
obtained regardless of their stability, so that finally the spectrum of stable
and unstable solutions in the specified parameter range is fully revealed. The
method is demonstrated for the GL equation in a three-dimensional
superconducting domain with an inhomogeneous magnetic field, a numerically
demanding problem known to have an involved solution landscape.

33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci