Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The derivative nonlinear Schr\"odinger equation on the half-line   We analyze the derivative nonlinear Schr\"odinger equation $iq_t + q_{xx} =
i(|q|^2q)_x$ on the half-line using the Fokas method. Assuming that the
solution $q(x,t)$ exists, we show that it can be represented in terms of the
solution of a matrix Riemann-Hilbert problem formulated in the plane of the
complex spectral parameter $\zeta$. The jump matrix has explicit $x,t$
dependence and is given in terms of the spectral functions $a(\zeta)$,
$b(\zeta)$ (obtained from the initial data $q_0(x) = q(x,0)$) as well as
$A(\zeta)$, $B(\zeta)$ (obtained from the boundary values $g_0(t) = q(0,t)$ and
$g_1(t) = q_x(0,t)$). The spectral functions are not independent, but related
by a compatibility condition, the so-called global relation. Given initial and
boundary values $\{q_0(x), g_0(t), g_1(t)\}$ such that there exist spectral
function satisfying the global relation, we show that the function $q(x,t)$
defined by the above Riemann-Hilbert problem exists globally and solves the
derivative nonlinear Schr\"odinger equation with the prescribed initial and
boundary values.

33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
16
The categories of this paper are: stat
2
The categories of this paper are: math