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 introduce the Dunkl--Klein--Gordon (DKG) equation in 2D by changing standard partial derivatives Dunkl Klein--Gordon (KG) equation. show that generalization with derivative of $z$-component angular momentum is what allows separation variables DKG Then, we compute energy spectrum and eigenfunctions equations for Coulomb potential oscillator analytically from an ${\rm su}(1,1)$ algebraic point...

For the one-dimensional nonlinear damped Klein-Gordon equation \[ \partial_{t}^{2}u+2\alpha\partial_{t}u-\partial_{x}^{2}u+u-|u|^{p-1}u=0 \quad \mbox{on $\mathbb{R}\times\mathbb{R}$,}\] with $\alpha>0$ and $p>2$, we prove that any global finite energy solution either converges to $0$ or behaves asymptotically as $t\to \infty$ sum of $K\geq 1$ decoupled solitary waves. In multi-soliton case 2$, ...

Herein, the Dirac equation is compared with the KleinGordon equation. In contrast to the Dirac case, it is proved that the Klein-Gordon equation has difficulties with the Hamiltonian differential operator of relativistic quantum mechanics and with the definition of an inner product of wave functions, which is a requirement for a construction of a Hilbert space. An added discussion of the Pauli-...

In this paper we study existence and orbital stability for solitary waves of the nonlinear Klein-Gordon equation. The energy of these solutions travels as a localized packet, hence they are a particular type of solitons. In particular we are interested in sufficient conditions on the potential for the existence of solitons. Our proof is based on the study of the ratio energy/charge of a functio...

Relying on the variational principle, it is proved that new contradictions emerge from an analysis of the Lagrangian density of the Klein-Gordon field: normalization problems arise and interaction with external electromagnetic fields cannot take place. By contrast, the Dirac equation is free of these problems. Other inconsistencies arise if the KleinGordon field is regarded as a classical field.