[en] A one-component factorization of the Klein-Gordon operator is presented. The role of the factorizing matrices is played by certain (non-local) spatial reflection operators. (author)

[en] In the nonlinear field theory of the elementary particles particlelike spherically symmetrical solutions of non linear equations are usually investigated. There were also studied stringlike cylindrically symmetrical solutions and spatially one dimensional (plane) solutions in order to understand the unusual behavior of solitons which are interpreted as a prototype of elementary particles. In that way, for a qualitative study of the possibilities of the theory, simple solutions of non linear field equations are investigated (e.g. of the non linear Klein-Gordon equation). Moreover the non linearity is chosen according to the suitable mathematical model (sine-Gordon, Φ⁴-Theory, and so on). In this paper we consider the possibilities of intermediate type of solutions between spherically and cylindrically symmetrical or plane solutions. We investigated the non linear Klein-Gordon equation with non linearity of the step form

[en] In this paper the simple supersymmetric Wess-Zumino model is extended to arbitrary d = 4ν dimensions. The components of the quiral superfield are found to obey a higher order Klein-Gordon-type equation, whose Green functions is discussed

[en] In this note, we prove the instability of stationary states for the Schroedinger equation and for the Klein-Gordon equation. Here, u(x) is a ground state solution of the nonlinear scalar field equation -Δu+ωu=g(u) in Rsup(N). Indeed, under certain assumptions on g, we show that there exist initial conditions, arbitrarily close to the stationary states, such that the solutions of these equations blow up in finite time

[en] The propagator for the 2D heat equation in an arbitrary linear space is shown to give solutions of the two-component Kadomtsev-Petviashvilii (KP) equations, also called Davey-Stewartson system. This propagator is subject to the Klein-Gordon equation and its right-derivatives are required to be of rank one, that imply that it can be expressed in terms of solutions of the Dirac equation. Large families of solutions of the two-component Kadomtsev-Petviashvilii equations are constructed in terms of solutions of the heat and Dirac equations. Particular attention is paid to the real reductions of the Davey-Stewartson type, recovering in this way the line solitons and the multidromion solutions. Moreover, new solutions to the Davey-Stewartson I are presented as massive deformations of the dromion. (author)

[en] We generalize to the case of the Klein-Gordon equation results on the order of energy levels of the Schroedinger equation for a given sign of the Laplacian of the potential. In particular we obtain modified versions of the theorems on the order of energy levels for a negative, vector-like, central potential with a Laplacian of a given sign. For the case of a positive Laplacian, a positive scalar potential, with a positive Laplacian, can be included too. (Authors) 6 refs

[en] It is proved that the free Klein Gordon fields of spatial dimension >= 2 have no conservation laws expressible by differential polynomials with constant coefficients other than those found by Kibble. (Auth.)

No abstract available

[en] We study the time decay of finite energy solutions of the non linear Klein-Gordon (NLKG) equation in space dimension n >= 3, by using a reformulation of the original method of Morawetz and Strauss to the non linear Schroedinger (NLS) equation. We prove that such solutions satisfy some of the time decay properties of the solutions of the free equation. Our results extend those of Brenner. We also improve the results for the NLS equation. As an intermediate result, we obtain boundedness properties in time (in a suitable sense) of finite energy solutions of both equations under fairly weak assumptions on f

[en] We study the Klein-Gordon symbolic calculus of operators acting on solutions of the free Klein-Gordon equation. It contracts to the Weyl calculus as c→∞. Mathematically, it may also be considered as a pseudodifferential analysis on the unit ball of Rⁿ