# Dynamics of the nonlinear Klein–Gordon equation in the nonrelativistic limit

@article{Pasquali2017DynamicsOT, title={Dynamics of the nonlinear Klein–Gordon equation in the nonrelativistic limit}, author={Stefano Pasquali}, journal={Annali di Matematica Pura ed Applicata (1923 -)}, year={2017}, volume={198}, pages={903-972} }

We study the nonlinear Klein–Gordon (NLKG) equation on a manifold M in the nonrelativistic limit, namely as the speed of light c tends to infinity. In particular, we consider a higher-order normalized approximation of NLKG (which corresponds to the NLS at order $$r=1$$r=1) and prove that when M is a smooth compact manifold or $$\mathbb {R}^d$$Rd, the solution of the approximating equation approximates the solution of the NLKG locally uniformly in time. When $$M=\mathbb {R}^d$$M=Rd, $$d \ge 2$$d…

## 7 Citations

### On comparison of asymptotic expansion techniques for nonlinear Klein-Gordon equation in the nonrelativistic limit regime

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This work concerns the time averaging techniques for the nonlinear Klein-Gordon (KG) equation in the nonrelativistic limit regime which have recently gained a lot of attention in numerical analysis.…

### Complex valued semi-linear heat equations in super-critical spaces $$E^s_\sigma $$

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We consider the Cauchy problem for the complex valued semi-linear heat equation where m ≥ 2 is an integer and the initial data belong to super-critical spaces E sσ for which the norms are deﬁned by…

### Almost global existence for the nonlinear Klein-Gordon equation in the nonrelativistic limit

- Mathematics
- 2017

We study the one-dimensional nonlinear Klein-Gordon equation with a convolution potential, and we prove that solutions with small Hs norm remain small for long times. The result is uniform with…

### Metastability phenomena in two-dimensional rectangular lattices with nearest-neighbour interaction

- MathematicsNonlinearity
- 2021

We study analytically the dynamics of two-dimensional rectangular lattices with periodic boundary conditions. We consider anisotropic initial data supported on one low-frequency Fourier mode. We show…

### On global behaviour of classical effective field theories

- Mathematics
- 2022

We continue the rigorous study of classical eﬀective ﬁeld theories (EFTs) that was recently initiated in the work of Reall and Warnick [RW22]. We study a system with one light and one heavy ﬁeld with…

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