The derivative nonlinear Schrödinger equation on the half-line
| dc.creator | Lenells, Jonatan | |
| dc.date | 2008-08-11 | |
| dc.date.accessioned | 2026-07-07T09:56:01Z | |
| dc.date.available | 2026-07-07T09:56:01Z | |
| dc.description | We analyze the derivative nonlinear Schrödinger 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 $ζ$. The jump matrix has explicit $x,t$ dependence and is given in terms of the spectral functions $a(ζ)$, $b(ζ)$ (obtained from the initial data $q_0(x) = q(x,0)$) as well as $A(ζ)$, $B(ζ)$ (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 Schrödinger equation with the prescribed initial and boundary values. | |
| dc.description | 27 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/0808.1534 | |
| dc.identifier | http://arxiv.org/abs/0808.1534 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166835 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | The derivative nonlinear Schrödinger equation on the half-line | |
| dc.type | text |