Kink internal modes in discrete nonlinear chains

Internal modes of sine-Gordon solitons in the presence of spatiotemporal perturbations

We investigate the dynamics of the sine-Gordon solitons perturbed by spatiotemporal external forces. We prove the existence of internal (shape) modes of sine-Gordon solitons when they are in the presence of inhomogeneous space-dependent external forces, provided some conditions (for these forces) hold. Additional periodic time-dependent forces can sustain oscillations of the soliton width. We show that, in some cases, the internal mode even can become unstable, causing the soliton to decay into an antisoliton and two solitons. In general, in the presence of spatiotemporal forces the soliton behaves as a deformable (nonrigid) object. A soliton moving in an array of inhomogeneities can also present sustained oscillations of its width. There are very important phenomena (like the soliton-antisoliton collisions) where the existence of internal modes plays a crucial role.

Solitonic structures in a nonlinear model with interparticle anharmonic interaction

Using a special combination of relevant parameters for a model with interparticle anharmonic interactions, we can predict the appearance of solitonic structures. The most remarkable representatives of the structures found here are the so-called drop compactons, (solitons with compact support in the shape of hard spheres), cusps, peak solitons (peakons), and defects. These analytic solutions (similar to others in their family) are obtained by considering strong restrictions on the possible values of their velocities. We analyze two types of physical boundary condition: the trivial and the so-called condensate boundary conditions. The total energy concentrated in each soliton pattern is also calculated.

Driven kink in the frenkel-kontorova model

The dynamics of dc driven chain of harmonically interacting atoms in the external sinusoidal potential (the Frenkel-Kontorova model) is studied. It is shown that in the underdamped case the motion of the topological soliton (kink) becomes unstable at a high velocity due to excitation of the localized intrinsic kink mode (the discrete shape mode, or discrete breather) in the kink tail. When the amplitude of the breather's oscillation becomes large enough, it decays into a kink-antikink pair. The subsequent collision of newly created kink and antikink leads to a sharp transition to the running state, where all atoms of the chain slide over the external potential almost freely.

Existence of internal modes of sine-gordon kinks

We study whether or not sine-Gordon kinks exhibit internal modes or "quasimodes." By considering the response of the kinks to ac forces and initial distortions, we show that neither intrinsic internal modes nor "quasimodes" exist in contrast to previous reports. However, we do identify a different kind of internal mode bifurcating from the bottom edge of the phonon band which arises from the discretization of the system in the numerical simulations, thus confirming recent predictions.

Motion of compactonlike kinks

We analyze the ability of a compactonlike kink (i.e., kink with compact support) to execute a stable ballistic propagation in a discrete Klein-Gordon system with anharmonic coupling. We demonstrate that the effects of lattice discreteness, and the presence of a linear coupling between lattice sites, are detrimental to a stable ballistic propagation of the compacton, because of the particular structure of the small-oscillation frequency spectrum of the compacton in which the lower-frequency internal modes enter in direct resonance with phonon modes. Our study reveals the parameter regions for obtaining a stable ballistic propagation of a compactonlike kink. Finally we investigate the interactions between compactonlike kinks.