In this paper we construct the scattering operator for the forced non-linear Schr odinger equation with a potential on the half-line. Moreover, in the case where the force is zero, and the solutions satisfy the homogeneous Dirichlet boundary condition at zero, we prove that the scattering operator d
The forced non-linear Schrödinger equation with a potential on the half-line
✍ Scribed by Ricardo Weder
- Publisher
- John Wiley and Sons
- Year
- 2005
- Tongue
- English
- Weight
- 185 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.637
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
In this paper I prove a L p &L p estimate for the solutions to the one-dimensional Schro dinger equation with a potential in L 1 # where in the generic case #>3Â2 and in the exceptional case (i.e., when there is a half-bound state of zero energy) #>5Â2. I use this estimate to construct the scatterin
## Abstract In this paper we consider the inverse scattering problem for the non‐linear Schrödinger equation on the line \def\dr{{\rm d}}$$i{\partial\over\partial t}u(t,x)=‐{\dr^2\over\dr x^2}u(t,x)+V\_0(x)u(t,x)+\sum\_{j=1}^{\infty}V\_j(x)|u|^{2(j\_0+j)}u(t,x)$$\nopagenumbers\end We prove, unde
## Abstract We consider the scattering problem for the fourth‐order non‐linear Schrödinger‐type equation: equation image We show the existence of the modified wave operators for the above equation with cubic case by imposing the mean zero condition for the final data. Copyright © 2006 John Wiley
## Communicated by A. Kirsch In this study in the interval (0; +∞) a fundamental system of solutions with behavior at the neighborhood of zero and at infinity are investigated for the polynomial pencil of the matrix Schrödinger equation. The integral representations are constructed for the Jost-ty