Tomáš Dohnal
Localized Modes of the Linear Periodic Schr\"{o}dinger Operator with a Nonlocal Perturbation.
Tue, 08/25/2009 - 22:41 — SomNambulAuthors: Tomáš Dohnal, Michael Plum, Wolfgang Reichel
Subjects: Spectral Theory
AbstractWe consider the existence of localized modes corresponding to eigenvalues of
the periodic Schr\"{o}dinger operator $-\partial_x^2+ V(x)$ with an interface.
The interface is modeled by a jump either in the value or the derivative of
$V(x)$ and, in general, does not correspond to a localized perturbation of the
perfectly periodic operator. The periodic potentials on each side of the
interface can, moreover, be different. As we show, eigenvalues can only occur
in spectral gaps.Perfectly Matched Layers for Coupled Nonlinear Schr\"{o}dinger Equations with Mixed Derivatives.
Tue, 08/25/2009 - 22:41 — SomNambulAuthors: Tomáš Dohnal
Subjects: Numerical Analysis
AbstractThis paper constructs perfectly matched layers (PML) for a system of 2D
Coupled Nonlinear Schr\"odinger equations with mixed derivatives which arises
in the modeling of gap solitons in nonlinear periodic structures with a
non-separable linear part. The PML construction is performed in Laplace Fourier
space via a modal analysis and can be viewed as a complex change of variables.
The mixed derivatives cause the presence of waves with opposite phase and group
velocities, which has previously been shown to cause instability of layer
equations in certain types of hyperbolic problems.- Read more
- 2 comments
- login or register to post comments
User login
