Biphonons in the Klein-Gordon lattice

Moving kinks and nanopterons in the nonlinear Klein-Gordon lattice

We study moving topological solitons (kinks and antikinks) in the nonlinear KleinGordon chain. These solitons are shown to exist with both monotonic (non-oscillating) and oscillating asymptotics (tails). Using the pseudo-spectral method, the (anti)kink solutions with oscillating background (so-called nanopterons) are found as travelling waves of permanent profile propagating with constant veloc...

Two-phonon pseudogap in the Klein-Gordon lattice

– The energy spectrum of the quantum Klein-Gordon (KG) lattice is computed numerically for model parameters relevant to optical phonon spectra. A pairing of phonon states is found when nonlinearity is significant, which agrees with other studies on different quantum lattice models [1, 2]. It results from the lattice anharmonicity, the magnitude of which is quantified by the binding energy of ph...

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION

Quantum breathers in a nonlinear Klein Gordon lattice

The quantum modes of a nonlinear Klein Gordon lattice have been computed numerically [L. Proville, Phys. Rev. B 71, 104306 (2005)]. The on-site nonlinearity has been found to lead to a phonon pairing and consequently some phonon bound states. In the present paper, the time dependent Wannier transform of these states is shown to exhibit a breather-like behavior, i.e., it is spatially localized a...

Analytical solutions for the fractional Klein-Gordon equation

In this paper, we solve a inhomogeneous fractional Klein-Gordon equation by the method of separating variables. We apply the method for three boundary conditions, contain Dirichlet, Neumann, and Robin boundary conditions, and solve some examples to illustrate the effectiveness of the method.