Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A solvable string on a Lorentzian surface   It is shown that there are nonlinear sigma models which are Darboux
integrable and possess a solvable Vessiot group in addition to those whose
Vessiot groups are central extensions of semi-simple Lie groups. They govern
harmonic maps between Minkowski space $\mathbb{R}^{1,1}$ and certain complete,
non-constant curvature 2-metrics. The solvability of the Vessiot group permits
a reduction of the general Cauchy problem to quadrature. We treat the specific
case of harmonic maps from Minkowski space into a non-constant curvature
Lorentzian 2-metric, $\boldsymbol{\lambda}$. Despite the completeness of
$\boldsymbol{\lambda}$ we exhibit a Cauchy problem with real analytic initial
data which blows up in finite time. We also derive a hyperbolic Weierstrass
representation formula for all harmonic maps from $\mathbb{R}^{1,1}$ into
$\boldsymbol{\lambda}$.

34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org