ac driven sine-Gordon solitons: dynamics and stability

Directed motion of topological solitons (kinks or antikinks) in the damped and AC-driven discrete sine-Gordon system is investigated. We show that if the driving field breaks certain time-space symmetries, the soliton can perform unidirectional motion. The phenomenon resembles the well known effects of ratchet transport and nonlinear harmonic mixing. Direction of the motion and its velocity depends on the shape of the AC drive. Necessary conditions for the occurrence of the e...

We present in closed form some special travelling-wave solutions (on the real line or on the circle) of a perturbed sine-Gordon equation. The perturbation of the equation consists of a constant forcing term $\gamma$ and a linear dissipative term, and the equation is used to describe the Josephson effect in the theory of superconductors and other remarkable physical phenomena. We determine all travelling-wave solutions with unit velocity (in dimensionless units). For $|\gamma|...

We consider a spatially non-autonomous discrete sine-Gordon equation with constant forcing and its continuum limit(s) to model a 0-$\pi$ Josephson junction with an applied bias current. The continuum limits correspond to the strong coupling limit of the discrete system. The non-autonomous character is due to the presence of a discontinuity point, namely a jump of $\pi$ in the sine-Gordon phase. The continuum models admits static solitary waves which are called $\pi$-kinks and...

We demonstrate numerically that an oscillation mode in 1+1 dimensions (eg a breather or an oscillon) can decay into a kink-antikink pair by a sudden distortion of the evolution potential which occurs within a certain time or space domain. In particular, we consider the transition of a sine-Gordon potential into a \Phi^4 potential. The breather field configuration is assumed to initially evolve in a sine-Gordon potential with velocity $v$ and oscillation frequency $\omega$. We...

Nonlinear waves that collide with localized defects exhibit complex behavior. Apart from reflection, transmission, and annihilation of an incident wave, a local inhomogeneity can activate internal modes of solitons, producing many impressive phenomena. In this work, we investigate a two-dimensional sine-Gordon model perturbed by a family of localized forces. We observed the formation of bubble-like and drop-like structures due to local internal shape modes instabilities. We d...

A parametrically forced sine-Gordon equation with a fast periodic {\em mean-zero} forcing is considered. It is shown that $\pi$-kinks represent a class of solitary-wave solutions of the equation. This result is applied to quasi-one-dimensional ferromagnets with an easy plane anisotropy, in a rapidly oscillating magnetic field. In this case the $\pi$-kink solution we have introduced corresponds to the uniform ``true'' domain wall motion, since the magnetization directions on o...

To study the propagation of nonlinear waves across Y- and T-type junctions, we consider the 2D sine--Gordon equation as a model and study the dynamics of kinks and breathers in such geometries. The comparison of the energies reveals that the angle of the fork plays no role. Motivated by this, we introduce a 1D effective equation whose solutions agree well with the 2D simulations for kink and breather solutions. For branches of equal width, breather crossing occurs approximate...

We consider the sine-Gordon equation on metric graphs with simple topologies and derive vertex boundary conditions from the fundamental conservation laws, such as energy and current conservation. Traveling wave solutions for star and tree graphs are obtained analytically in the form of kink, antikink and breather solitons for a special case. It is shown that these solutions provide reflectionless soliton transmission at the graph vertex. We find the sum rule for bond-dependen...

In the present work the evolution of a coherent field structure of the Sine-Gordon equation under quantum fluctuations is studied. The basic equations are derived from the coherent state approximation to the functional Schr\"odinger equation for the field. These equations are solved asymptotically and numerically for three physical situations. The first is the study of the nonlinear mechanism responsible for the quantum stability of the soliton in the presence of low momentum...

We report analytical and numerical results on breather-like field configurations in a theory which is a deformation of the integrable sine-Gordon model in (1+1) dimensions. The main motivation of our study is to test the ideas behind the recently proposed concept of quasi-integrability, which emerged from the observation that some field theories present an infinite number of quantities which are asymptotically conserved in the scattering of solitons, and periodic in time in t...