In this paper we consider the Klein—Gordon—Maxwell system in electrostatic case, assuming fall-off large-distance requirement on gauge potential. We are interested proving existence of finite energy (and charge) standing waves, having phase corresponding to mass coefficient Klein—Gordon Lagrangian.

In this paper, based on sinh-cosh method and sinh-Gordon expansion method,families of solutions of (2+1)-dimensional breaking soliton equation are obtained.These solutions include Jacobi elliptic function solution, soliton solution,trigonometric function solution.

Antinuclear antibodies (ANA) were demonstrated in 3 out of 10 Gordon setters with symmetrical lupoid onychodystrophy and in 5 out of 13 Gordon setters with black hair follicular dysplasia. Two dogs showed both symmetrical lupoid onychodystrophy and black hair follicular dysplasia, and one of these was ANA positive. The results suggest that symmetrical lupoid onychodystrophy and black hair folli...

We study the scattering theory for charged Klein-Gordon equations:  (∂t − iv(x))2φ(t, x) + (x,Dx)φ(t, x) = 0, φ(0, x) = f0, i−1∂tφ(0, x) = f1, where: (x,Dx) = − ∑ 1≤j,k≤n ( ∂xj − ibj(x) ) a(x) (∂xk − ibk(x)) +m (x), describing a Klein-Gordon field minimally coupled to an external electromagnetic field described by the electric potential v(x) and magnetic potential ~b(x). The flow of the Kle...

Laplace operators on metric graphs give rise to Klein-Gordon and wave operators. Solutions of the Klein-Gordon equation and the wave equation are studied and finite propagation speed is established. Massive, free quantum fields are then constructed, whose commutator function is just the Klein-Gordon kernel. As a consequence of finite propagation speed Einstein causality (local commutativity) ho...

It is proved that no Hamiltonian exists for the real Klein-Gordon field used in the Yukawa interaction. It is also shown that a real Klein-Gordon particle can be neither in a free isolated state nor in a bound state having an angular momentum l > 0. The experimental data support these conclusions. This outcome is in a complete agreement with Dirac's negative opinion on the Klein-Gordon equation.

It is well known that the classical string on a two-sphere is more or less equivalent to the sine-Gordon model. We consider a system which can be understood as a T-dual to the classical string on a two-sphere. We show that there is a projection map from the phase space of this model to the phase space of the sine-Gordon model. The corresponding Poisson structure of the sine-Gordon model is nonl...

We consider the problem of construction of graphs with given degree k and girth 5 and as few vertices as possible. We give a construction of a family of girth 5 graphs based on relative difference sets. This family contains the smallest known graph of degree 8 and girth 5 which was constructed by G. Royle, four of the known cages including the Hoffman-Singleton graph, some graphs constructed by...