# From the Klein–Gordon–Zakharov system to the Klein–Gordon equation

@article{Daub2016FromTK, title={From the Klein–Gordon–Zakharov system to the Klein–Gordon equation}, author={Markus Daub and Guido Schneider and Katharina Schratz}, journal={Mathematical Methods in the Applied Sciences}, year={2016}, volume={39}, pages={5371 - 5380} }

In a singular limit, the Klein–Gordon (KG) equation can be derived from the Klein–Gordon–Zakharov (KGZ) system. We point out that for the original system posed on a d‐dimensional torus, the solutions of the KG equation do not approximate the solutions of the KGZ system. The KG system has to be modified to make correct predictions about the dynamics of the KGZ system. We explain that this modification is not necessary for the approximation result for the whole space Rd with d≥3. Copyright © 2016…

## 12 Citations

Effective Numerical Simulation of the Klein–Gordon–Zakharov System in the Zakharov Limit

- Mathematics, Computer Science
- 2020

The idea is to filter out the highly oscillatory phases explicitly in the solution to play back the numerical task to solving the non-oscillatory Zakharov limit system and show that this method is more effective than other methods in the high-plasma frequency regime c ≫ 1.

The Dirac-Klein-Gordon system in the strong coupling limit

- Mathematics, Physics
- 2021

We study the Dirac equation coupled to scalar and vector Klein-Gordon fields in the limit of strong coupling and large masses of the fields. We prove convergence of the solutions to those of a cubic…

Uniformly Accurate Methods for Klein-Gordon type Equations

- Mathematics
- 2018

The main contribution of this thesis is the development of a novel class of uniformly accurate methods for Klein–Gordon type equations. Klein–Gordon type equations in the non-relativistic limit…

A uniformly and optimally accurate multiscale time integrator method for the Klein-Gordon-Zakharov system in the subsonic limit regime

- MathematicsComput. Math. Appl.
- 2018

On the dynamics of the mean-field polaron in the high-frequency limit

- Mathematics
- 2017

We consider the dynamics of the mean-field polaron in the limit of infinite phonon frequency $$\omega \rightarrow \infty $$ω→∞. This is a singular limit formally leading to a Schrödinger–Poisson…

A uniformly and optimally accurate method for the Klein-Gordon-Zakharov system in simultaneous high-plasma-frequency and subsonic limit regime

- Mathematics
- 2019

We present a uniformly and optimally accurate numerical method for solving the Klein-Gordon-Zakharov (KGZ) system with two dimensionless parameters $0<\epsilon\le1$ and $0<\gamma\le 1$, which are…

Uniform error bounds of a finite difference method for the Klein-Gordon-Zakharov system in the subsonic limit regime

- MathematicsMath. Comput.
- 2018

The main techniques in the analysis include the energy method, cut-off of the nonlinearity to bound the numerical solution, the integral approximation of the oscillatory term, and $\varepsilon$-dependent error bounds between the solutions of KGZ and its limiting model when $\varpsilon\to0^+$.

Failure of the N‐wave interaction approximation without imposing periodic boundary conditions

- MathematicsZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
- 2020

The N‐wave interaction (NWI) system appears as an amplitude system in the description of N nonlinearly interacting and linearly transported wave packets in dispersive wave systems such as the water…

Effective Slow Dynamics Models for a Class of Dispersive Systems

- Mathematics, Computer ScienceJournal of Dynamics and Differential Equations
- 2019

The abstract approximation theorem applies to a number of semilinear systems, such as the Dirac–Klein–Gordon system, the Klein–Gordon–Zakharov system, and a mean field polaron model.

A uniformly first-order accurate method for Klein-Gordon-Zakharov system in simultaneous high-plasma-frequency and subsonic limit regime

- Computer ScienceJ. Comput. Phys.
- 2021

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