Wave Phenomena

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In s.kit.edu/mizkw3lc we derive properties of the Calderon operator which is the analogue of the Dirichlet-to-Neumann operator for the scalar Helmholtz equation. We consider the cases where the boundary data decay or are quasi-periodic along the cylinder axis. #CRC1173

In s.kit.edu/zkkjic32 we study Maxwell’s equations with periodic coefficients (or local perturbations of periodic coefficients) in a closed waveguide. Particular emphasis is put on the radiation condition which follows from the limiting absorption principle. #CRC1173

In the #CRC1173 preprint s.kit.edu/wzzjwj0j we study Maxwell's equations for a Kerr-type optical material with instantaneous response that is of cylindrical or slab geometry. We show existence of breather solutions using variational methods.

In s.kit.edu/lzilhhzg we derive radiation conditions for the Helmholtz equation in a closed wave-guide with periodic coefficients from the limiting absorption principle. We characterize the set of all bounded solutions of the homogeneous problem. #CRC1173

In our #CRC1173 preprint s.kit.edu/m5wk4m1k we propose a multiscale approach for discrete minimizers of the Ginzburg-Landau energy. We choose different meshes and ansatz spaces for the order parameter and the vector potential and thus derive error bounds of optimal order.

In s.kit.edu/j0mxzdkj we study the magnetohydrodynamics equations in the non-resistive limit. We establish stability of small perturbations near an affine shear flow and a large constant magnetic field and show growth of the magnetic field. #CRC1173

In our #CRC1173 preprint s.kit.edu/g4j32j3m we study the space and time discretization of Maxwell equations with an external surface current. This is the first step to simulate the interaction of Graphene with light pulses.

In the #CRC1173 preprint s.kit.edu/jcyhlmwy we present an IMEX scheme for semilinear wave equations. Our main results are error bounds of the full discretization combined with a general abstract space discretization.

In s.kit.edu/g3hhzzzy, we compare old and new Kirchhoff migration/inversion formulas for seismic tomography wrt their imaging properties. To this end, we analyze these formulas microlocally and illustrate the theoretical results with numerical examples. #CRC1173

Delving into multi-scale effects of thermal radiative transfer equations and their computational challenges, a novel asymptotic-preserving & rank-adaptive dynamical low-rank scheme in s.kit.edu/jxgxz3m1 captures the correct limit with low memory requirements. #CRC1173

Our new preprint s.kit.edu/jwim3zcw on high-frequency wave propagation in nonlinear media is online. We prove new error bounds for the slowly varying envelope approximation and a related model. This is the result of years of work, and we are now very happy. #CRC1173

In the #CRC1173 preprint s.kit.edu/z1m2j3jy we obtain existence and decay of small solutions in the viscoelastic Klein-Gordon equation for large periods of time. This result extends previous work on the half Klein-Gordon equation.

In our #CRC1173 preprint s.kit.edu/mkzlzidj we study the space and time discretization of the Kuznetsov equation, a classical wave model of nonlinear acoustics. We show optimal order of convergence uniformly in the vanishing sound diffusivity parameter.

Magnetic Schrödinger operators cannot have bound states in the continuum (BIC) under natural conditions solely on the magnetic field and potential and not on the vector potential. The Miller-Simon examples show that our condition in s.kit.edu/3zij2zmz is sharp. #CRC1173

In s.kit.edu/zkxzll2y we study the existence and dynamical stability of solitary waves in the Lugiato-Lefever equation. The solutions under consideration are highly nonlinear, localized waves and model Kerr frequency combs in nonlinear optics. #CRC1173

In s.kit.edu/xkycxzg5 we study time integration schemes for the 3D energy-(sub)critical semilinear wave equation. We use discrete-time Strichartz estimates to show first-order convergence for the Lie splitting and convergence order 3/2 for a corrected Lie splitting. #CRC1173

In s.kit.edu/cwyjm2mj we study the magnetohydrodynamics equations with viscosity and horizontal resistivity. We establish stability of small perturbations near a combination of an affine shear flow and a large constant magnetic field. #CRC1173

In s.kit.edu/y1xjc2kz we give a proof of nonlinear Landau damping. Different time scales are shown to result in constrained plasma echo chains and different optimal regularity classes. #CRC1173

In our recent preprint s.kit.edu/jc5jlijl, we consider Gaussian wave packets for the magnetic Schrödinger equation which reduce the computational effort dramatically. We prove convergence of the approximation and thereby generalize known results from the literature. #CRC1173