25 citations · 122 across the 23 of their papers we have counts for
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Polychromatic Localized Waves with Complex Frequencies in Nonlinear Maxwell Equations with Material Dispersion
Tomas Dohnal, Maximilian Hanisch, Runan He
We study the existence of polychromatic solutions of cubically nonlinear Maxwell equations in the whole space and with dispersive media, i.e., with a time delayed polarization. Due…
Traveling modulating pulse solutions with small tails for a nonlinear wave equation in periodic media
Tomas Dohnal, Dmitry E. Pelinovsky, Guido Schneider
Traveling modulating pulse solutions consist of a small amplitude pulse-like envelope moving with a constant speed and modulating a harmonic carrier wave. Such solutions can be app…
Well-Posedness and Exponential Stability of Nonlinear Maxwell Equations for Dispersive Materials with Interface
Tomáš Dohnal, Mathias Ionescu-Tira, Marcus Waurick
In this paper we consider an abstract Cauchy problem for a Maxwell system modelling electromagnetic fields in the presence of an interface between optical media. The electric polar…
Justification of the Asymptotic Coupled Mode Approximation of Out-of-Plane Gap Solitons in Maxwell Equations
Tomáš Dohnal, Giulio Romani
In periodic media gap solitons with frequencies inside a spectral gap but close to a spectral band can be formally approximated by a slowly varying envelope ansatz. The ansatz is b…
Eigenvalue Bifurcation in Doubly Nonlinear Problems with an Application to Surface Plasmon Polaritons
Tomáš Dohnal, Giulio Romani
We consider a class of generally non-self-adjoint eigenvalue problems which are nonlinear in the solution as well as in the eigenvalue parameter ("doubly" nonlinear). We prove a bi…
Bifurcation of Gap Solitons in Coupled Mode Equations in Dimensions
Tomas Dohnal, Lisa Wahlers
We consider a system of first order coupled mode equations in describing the envelopes of wavepackets in nonlinear periodic media. Under the assumptions of a spectra…