Tomáš Dohnal
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View article: Spectrum of the Maxwell Equations for a Flat Interface Between Homogeneous Dispersive Media
Spectrum of the Maxwell Equations for a Flat Interface Between Homogeneous Dispersive Media Open
The paper determines and classifies the spectrum of a non-self-adjoint operator pencil generated by the time-harmonic Maxwell problem with a nonlinear dependence on the frequency for the case of two homogeneous materials joined at a planar…
View article: Bifurcation and asymptotics of cubically nonlinear transverse magnetic surface plasmon polaritons
Bifurcation and asymptotics of cubically nonlinear transverse magnetic surface plasmon polaritons Open
Linear Maxwell equations for transverse magnetic (TM) polarized fields support single frequency surface plasmon polaritons (SPPs) localized at the interface of a metal and a dielectric. Metals are typically dispersive, i.e. the dielectric …
View article: Travelling modulating pulse solutions with small tails for a nonlinear wave equation in periodic media
Travelling modulating pulse solutions with small tails for a nonlinear wave equation in periodic media Open
Travelling 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 approximated by solitons of an effective nonlinear Schrödinge…
View article: Bifurcation and Asymptotics of Cubically Nonlinear Transverse Magnetic Surface Plasmon Polaritons
Bifurcation and Asymptotics of Cubically Nonlinear Transverse Magnetic Surface Plasmon Polaritons Open
Linear Maxwell equations for transverse magnetic (TM) polarized fields support single frequency surface plasmon polaritons (SPPs) localized at the interface of a metal and a dielectric. Metals are typically dispersive, i.e. the dielectric …
View article: Well-posedness and exponential stability of nonlinear Maxwell equations for dispersive materials with interface
Well-posedness and exponential stability of nonlinear Maxwell equations for dispersive materials with interface Open
In this paper we consider an abstract Cauchy problem for a Maxwell system modeling electromagnetic fields in the presence of an interface between optical media. The electric polarization is in general time-delayed and nonlinear, turning th…
View article: Traveling modulating pulse solutions with small tails for a nonlinear wave equation in periodic media
Traveling modulating pulse solutions with small tails for a nonlinear wave equation in periodic media Open
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 approximated by solitons of an effective nonlinear Schrodinger…
View article: Well-Posedness and Exponential Stability of Nonlinear Maxwell Equations for Dispersive Materials with Interface
Well-Posedness and Exponential Stability of Nonlinear Maxwell Equations for Dispersive Materials with Interface Open
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 polarization is in general time-delayed and nonlinear, turning t…
View article: Well-Posedness and Exponential Stability of Nonlinear Maxwell Equations for Dispersive Materials with Interface
Well-Posedness and Exponential Stability of Nonlinear Maxwell Equations for Dispersive Materials with Interface Open
View article: Correction to: Eigenvalue bifurcation in doubly nonlinear problems with an application to surface plasmon polaritons
Correction to: Eigenvalue bifurcation in doubly nonlinear problems with an application to surface plasmon polaritons Open
This erratum corrects some errors which appear in [Dohnal T., Romani G., Eigenvalue bifurcation in doubly nonlinear problems with an application to surface plasmon polaritons, Nonlinear Differ. Equ. Appl. 28, 9 (2021).]. In particular, it …
View article: Rigorous Envelope Approximation for Interface Wave-Packets in Maxwell's Equations with 2D Localization
Rigorous Envelope Approximation for Interface Wave-Packets in Maxwell's Equations with 2D Localization Open
We study transverse magnetic (vector valued) wave-packets in the time dependent Kerr nonlinear Maxwell's equations at the interface of two inhomogeneous dielectrics with an instantaneous material response. The resulting model is quasilinea…
View article: Spectrum of the Maxwell Equations for a Flat Interface between Homogeneous Dispersive Media
Spectrum of the Maxwell Equations for a Flat Interface between Homogeneous Dispersive Media Open
The paper determines and classifies the spectrum of a non-self-adjoint operator pencil generated by the time-harmonic Maxwell problem with a nonlinear dependence on the frequency for the case of two homogeneous materials joined at a planar…
View article: A quasilinear transmission problem with application to Maxwell equations with a divergence-free <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi mathvariant="script">D</mml:mi></mml:math>-field
A quasilinear transmission problem with application to Maxwell equations with a divergence-free -field Open
Maxwell equations in the absence of free charges require initial data with a divergence-free displacement field D. In materials in which the dependence D=D(E) is nonlinear the quasilinear problem ∇⋅D(E)=0 is hence to be solved. In many app…
View article: A quasilinear transmission problem with application to Maxwell equations with a divergence-free $\mathcal D$-field
A quasilinear transmission problem with application to Maxwell equations with a divergence-free $\mathcal D$-field Open
Maxwell equations in the absence of free charges require initial data with a divergence free displacement field $\mathcal D$. In materials in which the dependence $\mathcal D=\mathcal D(\mathcal E)$ is nonlinear the quasilinear problem $\n…
View article: Bifurcation of Gap Solitons in Coupled Mode Equations in d Dimensions
Bifurcation of Gap Solitons in Coupled Mode Equations in d Dimensions Open
We consider a system of first order coupled mode equations in $${\mathbb {R}}^d$$ describing the envelopes of wavepackets in nonlinear periodic media. Under the assumptions of a spectral gap and a generic assumption on the dispersion …
View article: Eigenvalue bifurcation in doubly nonlinear problems with an application to surface plasmon polaritons
Eigenvalue bifurcation in doubly nonlinear problems with an application to surface plasmon polaritons Open
View article: Eigenvalue bifurcation in doubly nonlinear problems with an application to surface plasmon polaritons
Eigenvalue bifurcation in doubly nonlinear problems with an application to surface plasmon polaritons Open
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 bifurcation result from simple isolated eigenvalues of the li…
View article: Coupled mode equations and gap solitons in higher dimensions
Coupled mode equations and gap solitons in higher dimensions Open
View article: NLS approximation for wavepackets in periodic cubically nonlinear wave problems in $\mathbb{R}^d$
NLS approximation for wavepackets in periodic cubically nonlinear wave problems in $\mathbb{R}^d$ Open
The dynamics of single carrier wavepackets in nonlinear wave problems over periodic structures can be often formally approximated by the constant coefficient nonlinear Schrödinger equation (NLS) as an effective model for the wavepacket env…
View article: A Bloch wave numerical scheme for scattering problems in periodic wave-guides
A Bloch wave numerical scheme for scattering problems in periodic wave-guides Open
We present a new numerical scheme to solve the Helmholtz equation in a wave-guide. We consider a medium that is bounded in the $x_2$-direction, unbounded in the $x_1$-direction and $\varepsilon$-periodic for large $|x_1|$, allowing differe…
View article: A Bloch wave numerical scheme for scattering problems in periodic wave-guides
A Bloch wave numerical scheme for scattering problems in periodic wave-guides Open
We present a new numerical scheme to solve the Helmholtz equation in a wave-guide. We consider a medium that is bounded in the x2-direction, unbounded in the x1-direction and ε-periodic for large |x1|, allowing different media on the left …
View article: Bifurcation of nonlinear bound states in the periodic Gross-Pitaevskii\n equation with PT-symmetry
Bifurcation of nonlinear bound states in the periodic Gross-Pitaevskii\n equation with PT-symmetry Open
The stationary Gross-Pitaevskii equation in one dimension is considered with\na complex periodic potential satisfying the conditions of the PT (parity-time\nreversal) symmetry. Under rather general assumptions on the potentials we prove\nb…
View article: Bifurcation of nonlinear bound states in the periodic Gross-Pitaevskii equation with PT-symmetry
Bifurcation of nonlinear bound states in the periodic Gross-Pitaevskii equation with PT-symmetry Open
The stationary Gross-Pitaevskii equation in one dimension is considered with a complex periodic potential satisfying the conditions of the PT (parity-time reversal) symmetry. Under rather general assumptions on the potentials we prove bifu…
View article: Justification of the coupled mode asymptotics for localized wavepackets in the periodic nonlinear Schrödinger equation
Justification of the coupled mode asymptotics for localized wavepackets in the periodic nonlinear Schrödinger equation Open
View article: Bifurcation of eigenvalues in nonlinear problems with antilinear symmetry
Bifurcation of eigenvalues in nonlinear problems with antilinear symmetry Open
Many physical systems can be described by eigenvalues of nonlinear equations and bifurcation problems with a linear part that is non-selfadjoint, e.g., due to the presence of loss and gain. The balance of these effects is reflected in an a…
View article: Ground states of a nonlinear curl-curl problem in cylindrically symmetric media
Ground states of a nonlinear curl-curl problem in cylindrically symmetric media Open
View article: Bifurcation of Nonlinear Bloch Waves from the Spectrum in the Gross–Pitaevskii Equation
Bifurcation of Nonlinear Bloch Waves from the Spectrum in the Gross–Pitaevskii Equation Open
View article: Justification of the Coupled Mode Asymptotics for Localized Wavepackets\n in the Periodic Nonlinear Schr\\"odinger Equation
Justification of the Coupled Mode Asymptotics for Localized Wavepackets\n in the Periodic Nonlinear Schr\\"odinger Equation Open
We consider wavepackets composed of two modulated carrier Bloch waves with\nopposite group velocities in the one dimensional periodic Nonlinear\nSchroedinger/Gross-Pitaevskii equation. These can be approximated by first\norder coupled mode…
View article: Dispersive homogenized models and coefficient formulas for waves in general periodic media
Dispersive homogenized models and coefficient formulas for waves in general periodic media Open
We analyze a homogenization limit for the linear wave equation of second order. The spatial operator is assumed to be of divergence form with an oscillatory coefficient matrix aε that is periodic with characteristic length scale ε; no spat…
View article: Bifurcation of nonlinear eigenvalues in problems with antilinear symmetry
Bifurcation of nonlinear eigenvalues in problems with antilinear symmetry Open
Many physical systems can be described by nonlinear eigenvalues and bifurcation problems with a linear part that is non-selfadjoint e.g. due to the presence of loss and gain. The balance of these effects is reflected in an antilinear symme…