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Photo of Dominic Scheider

Dr. Dominic Scheider

  • Englerstraße 2
    76131 Karlsruhe

Current List of Courses
Semester Titel Typ
Summer Semester 2020 Seminar
Winter Semester 2019/20 Proseminar
Summer Semester 2019 Seminar
Winter Semester 2018/19 Seminar
Summer Semester 2018 Proseminar
Winter Semester 2017/18 Lecture
Summer Semester 2017 Lecture
Proseminar

Research

In my PhD project, I analyse systems of two coupled nonlinear Helmholtz equations.
The goal is to prove the existence of solutions using tools from, e.g., variational calculus or bifurcation theory.

Why the Helmholtz equation? It is a fundamental equation in physics describing the propagation and scattering of waves. For more information, please visit the webpage of our research group.


In a current project, I focus on the construction of breather (that is, time-periodic and spatially localized) solutions of nonlinear wave-type equations.
Here the application of methods from the theory of stationary Helmholtz equations promises new existence results. Indeed, using a Fourier series ansatz, this leads to an infinite system of (stationary, coupled, nonlinear) Helmholtz equations for the coefficients  u_k . This strategy, first applied in the final chapter of my dissertation thesis, seems to promise (new) families of weakly localized breathers.


Publications and Preprints

Here you can find my dissertation thesis.

R. Mandel, D. Scheider: Dual Variational Methods for a Nonlinear Helmholtz System. NoDEA Nonlinear Differential Equations Appl. 25 (2018), no. 2, 25:13.

R. Mandel, D. Scheider: Bifurcations of nontrivial solutions of a cubic Helmholtz system. ANONA Advances in Nonlinear Analysis 9 (2019), no. 1, 1026 - 1045.

D. Scheider: Breather Solutions of the Cubic Klein-Gordon Equation, Preprint, to appear in Nonlinearity.

R. Mandel, D. Scheider: An annulus multiplier and applications to the limiting absorption principle for Helmholtz equations with a step potential, Preprint.

R. Mandel, D. Scheider: Variational methods for breather solutions of Nonlinear Wave Equations, Preprint.