6 papers
Existence of traveling breather solutions to cubic nonlinear Maxwell equations in waveguide geometries
Sebastian Ohrem, Wolfgang Reichel
We consider the full set of Maxwell equations in a slab or cylindrical waveguide with a cubically nonlinear material law for the polarization of the electric field. The nonlinear p…
Pinning in the extended Lugiato-Lefever equation
Lukas Bengel, Dmitry Pelinovsky, Wolfgang Reichel
We consider a variant of the Lugiato-Lefever equation (LLE), which is a nonlinear Schrödinger equation on a one-dimensional torus with forcing and damping, to which we add a first-…
Travelling waves for Maxwell's equations in nonlinear and nonsymmetric media
Jarosław Mederski, Wolfgang Reichel
We look for travelling wave fields satisfying Maxwell's equations…
A breather construction for a semilinear curl-curl wave equation with radially symmetric coefficients
Michael Plum, Wolfgang Reichel
We consider the semilinear curl-curl wave equation $s(x) \partial_t^2 U +\nabla\times\nabla\times U + q(x) U \pm V(x) |U|^{p-1} U = 0 \mbox{ for } (x,t)\in \mathbb{R}^3\times\mathb…
Ground States of a Nonlinear Curl-Curl Problem in Cylindrically Symmetric Media
Thomas Bartsch, Tomáš Dohnal, Michael Plum +1
We consider the nonlinear curl-curl problem in related to the nonlinear Maxwell equations for monochromatic fie…
Mesh-independent a priori bounds for nonlinear elliptic finite difference boundary value problems
P. J. McKenna, W. Reichel, A. Verbitsky
In this paper we prove mesh independent a priori -bounds for positive solutions of the finite difference boundary value problem $$ -Δ_h u = f(x,u) \mbox{ in } Ω_h, \quad…