Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Numerical Unified Transform Method for the Nonlinear Schr\"odinger
  equation on the half-line   We implement the Numerical Unified Transform Method to solve the Nonlinear
Schr\"odinger equation on the half-line. For so-called linearizable boundary
conditions, the method solves the half-line problems with comparable complexity
as the Numerical Inverse Scattering Transform solves whole-line problems. In
particular, the method computes the solution at any $x$ and $t$ without spatial
discretization or time stepping. Contour deformations based on the method of
nonlinear steepest descent are used so that the method's computational cost
does not increase for large $x,t$ and the method is more accurate as $x,t$
increase. Our ideas also apply to some cases where the boundary conditions are
not linearizable.

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The categories of this paper are: comp-gas
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The categories of this paper are: stat
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg