Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linearizable Initial-Boundary Value Problems for the sine-Gordon
  Equation on the Half-Line   A rigorous methodology for the analysis of initial boundary value problems on
the half-line, $0<x<\infty$, $t>0$, for integrable nonlinear evolution PDEs has
recently appeared in the literature. As an application of this methodology the
solution $q(x,t)$ of the sine-Gordon equation can be obtained in terms of the
solution of a $2\times 2$ matrix Riemann-Hilbert problem. This problem is
formulated in the complex $k$-plane and is uniquely defined in terms of the so
called spectral functions $a(k)$, $b(k)$, and $B(k)/A(k)$. The functions $a(k)$
and $b(k)$ can be constructed in terms of the given initial conditions $q(x,0)$
and $q_t(x,0)$ via the solution of a system of two {\it linear} ODE's, while
for \emph{arbitrary} boundary conditions the functions $A(k)$ and $B(k)$ can be
constructed in terms of the given boundary condition via the solution of a
system of four {\it nonlinear} ODEs. In this paper we analyse two
\emph{particular} boundary conditions: the case of constant Dirichlet data,
$q(0,t) = \chi$, as well as the case that $q_x(0,t)$, $\sin (q(0,t)/2)$, and
$\cos(q(0,t)/2)$ are linearly related by two constants $\chi_1$ and $\chi_2$.
We show that for these particular cases, the system of the above nonlinear ODEs
can be avoided, and $B(k)/A(k)$ can be computed explicitly in terms of
$\{a(k),b(k),\chi\}$ and $\{a(k),b(k), \chi_1, \chi_2\}$ respectively. Thus
these ``linearizable'' initial-boundary value problems can be solved with
absolutely the same level of efficiency as the classical initial value problem
of the line.

31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int