Usin the Painlev test, it is shown that the only interablc nonlinear Klein-Gordon equations ux,=f(u) with f a linear combination of exponentials are the Liouville, sine-Gordon (or sinh-Gordon) and Mikhailov equations. In particular, the double sine-Gordon equation is not interable.

We develop the local theory of surfaces immersed in the pseudo-Galilean space, a special type of Cayley-Klein spaces. We define principal, Gaussian, and mean curvatures. By this, the general setting for study of surfaces of constant curvature in the pseudo-Galilean space is provided. We describe surfaces of revolution of constant curvature. We introduce special local coordinates for surfaces of...

We study global dynamics for the focusing nonlinear Klein-Gordon equation with the energy-critical nonlinearity in two or higher dimensions when the energy equals the threshold given by the ground state of a mass-shifted equation, and prove that the solutions are divided into scattering and blowup. In short, the Kenig-Merle scattering/blowup dichotomy [10, 11] extends to the threshold energy in...

We give the governing equations for multiple scalar fields in a flat Friedmann-Robertson-Walker (FRW) background spacetime on all scales, allowing for metric and field perturbations up to second order. We then derive the Klein-Gordon equation at second order in closed form in terms of gaugeinvariant perturbations of the fields in the uniform curvature gauge. We also give a simplified form of th...

In this paper, the lattice Boltzmann method for convectiondiffusion equation with source term is applied directly to solve some important nonlinear complex equations, including nonlinear Schrödinger (NLS) equation, coupled NLS equations, Klein-Gordon equation and coupled Klein-Gordon-Schrödinger equations, by using complex-valued distribution function and relaxation time. Detailed simulations o...

We prove that the Maxwell-Klein-Gordon equations on R relative to the Coulomb gauge are locally well-posed for initial data in H for all ε > 0. This builds on previous work by Klainerman and Machedon [3] who proved the corresponding result for a model problem derived from the Maxwell-Klein-Gordon system by ignoring the elliptic features of the system, as well as cubic terms.

We study the well-posedness of the Dirac-Klein-Gordon system in one space dimension with initial data that are analytic in a strip around the real axis. It is proved that for short times t the radius of analyticity σ(t) of the solutions remains constant while for |t| → ∞ we obtain a lower bound σ(t) ≥ c/|t|5+ in the case of positive Klein-Gordon mass and σ(t) ≥ c/|t|8+ in the massless case.

We prove that in the nonrelativistic limit c → ∞, where c is the speed of light, solutions of the Klein-Gordon-Maxwell system on R 1+3 converge in the energy space C([0, T ]; H 1) to solutions of a Schrödinger-Poisson system, under appropriate conditions on the initial data. This requires the splitting of the scalar Klein-Gordon field into a sum of two fields, corresponding, in the physical int...