We discuss several aspects of singularities of the solutions of the partial differential equations of Klein–Gordon, Schrödinger and Dirac. In particular we analyze the fold type singularity, of the first and higher orders, and the related characteristic equations. We also consider the field equations as reduction of homogenous equations in higher dimensions, and discuss how singularities of the...

It is proved that density plays a crucial role in the structure of quantum field theory. The Dirac and the Klein-Gordon equations are examined. The results prove that the Dirac equation is consistent with density related requirements whereas the Klein-Gordon equation fails to do that. Experimental data support these conclusions.

We prove existence results for travelling waves in discrete, damped, dc-driven sine-Gordon equations with periodic boundary conditions.

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 derive the long-time decay in weighted norms for solutions of the discrete 3D Schrödinger and Klein-Gordon equations.

The long-time asymptotics is derived for solutions of the discrete 3dimensional Schrödinger and Klein–Gordon equations. §

We demonstrate that for the sine-Gordon theory at the free fermion point, the 2point correlation functions of the fields exp(iαΦ) for 0 < α < 1 can be parameterized in terms of a solution to a sinh-Gordon-like equation. This result is derived by summing over intermediate multiparticle states and using the form factors to express this as a Fredholm determinant. The proof of the differential equa...

We find that the fundamental quadratic form of classical string propagation in 2 + 1 dimensional constant curvature spacetimes solves the Sinh-Gordon equation, the Cosh-Gordon equation or the Liouville equation. We show that in both de Sitter and anti de Sitter spacetimes (as well as in the 2 + 1 black hole anti de Sitter spacetime), all three equations must be included to cover the generic str...

We introduce mountain-pass type arguments in the context of orbital instability for Klein-Gordon equations. Our aim is to illustrate on two examples how these arguments can be useful to simplify proofs and derive new results of orbital stability/instability. For a power-type nonlinearity, we prove that the ground states of the associated stationary equation are minimizers of the functional acti...