The discrete Klein-Gordon equation on a two-dimensional square lattice satisfies an ` 7→ `∞ dispersive bound with polynomial decay rate |t|−3/4. We determine the shape of the light cone for any choice of the mass parameter and relative propagation speeds along the two coordinate axes. Fundamental solutions experience the least dispersion along four lines interior to the light cone rather than a...

Abstract In this paper we investigate the small data global existence and pointwise decay of solutions to two systems coupled wave-Klein–Gordon equations in spatial dimensions. particular, consider critical (in sense time decay) semilinear nonlinearities for wave equation below-critical Klein–Gordon equation, a situation that has not been studied before context equations. An interesting feature...

We study the 2D coupled wave–Klein-Gordon systems with semilinear null nonlinearities Q0 and Qαβ. The main result states that solution to system exists globally provided initial data is small in some weighted Sobolev space, which does not necessarily have compact support, we also asymptotic behavior of solution. In particular, show optimal time decay scattering major difficulties lie slow natur...

Consider the Klein–Gordon–Zakharov equations in $${\mathbb {R}}^{1+2}$$ , and we are interested establishing small global solution to investigating pointwise asymptotic behavior of solution. The can be regarded as a coupled semilinear wave Klein–Gordon system with quadratic nonlinearities which do not satisfy null conditions, fact that components decay sufficiently fast makes it harder conduct ...

The orbital instability of ground state standing waves eφω(x) for the nonlinear Klein-Gordon equation has been known in the domain of all frequencies ω for the supercritical case and for frequencies strictly less than a critical frequency ωc in the subcritical case. We prove the strong instability of ground state standing waves for the entire domain above. For the case when the frequency is equ...