We prove that a free relativistic rotor (or rotator) Klein-Gordon field is massless. To this end, the magnitude of the centrifugal force and its associated quantum operator for a free particle with a circular motion are determined in Special Relativity. A partial differential equation including the centrifugal force operator is derived. Finally, from the conjunction of the above equation and th...

The discrete Klein-Gordon equation on a two-dimensional square lattice satisfies an ` 7→ `∞ dispersive bound with polynomial decay rate |t|−3/4. We determine the shape of the light cone for any choice of the mass parameter and relative propagation speeds along the two coordinate axes. Fundamental solutions experience the least dispersion along four lines interior to the light cone rather than a...

In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy analysis method (HAM).Comparisons are made between the Adomian decomposition method (ADM), the exact solution and homotopy analysis method. The results reveal that the proposed method is very effective and simple.

In this paper, the modified simple equation method is used to construct exact periodic and soliton solutions of some nonlinear partial differential equations. Exact solutions of the nonlinear Schrödinger equation, the Hamiltonian amplitude equation, Klein-Gordon equation in 1+2 dimension, the coupled Klein-Gordon equation, the (2 + 1)-dimensional long-wave-short-wave resonance interaction equat...