Exceptional discretisations of the sine-Gordon equation

Arbitrarily large numbers of kink internal modes in inhomogeneous sine-Gordon equations

We prove the existence of an infinite number of internal (shape) modes of sine-Gordon solitons in the presence of some inhomogeneous long-range forces, provided some conditions are satisfied.

Configurational entropy of generalized sine-Gordon-type models

A family of deformed models of the sine-Gordon-type can be generated by twisting the sine-Gordon model. As a particular case, the 3-sine-Gordon model is here addressed, whose differential configurational entropy and the differential configurational complexity of three topological sectors are discussed, using two complementary approaches. Stability aspects are also discussed.

Bistability in sine-Gordon: the ideal switch

The sine-Gordon equation, used as the representative nonlinear wave equation, presents a bistable behavior resulting from nonlinearity and generating hysteresis properties. We show that the process can be understood in a comprehensive analytical formulation and that it is a generic property of nonlinear systems possessing a natural band gap. The approach allows to discover that sine-Gordon can work as an it ideal switch by reaching a transmissive regime with vanishing driving amplitude.

Existence of travelling waves in discrete sine-Gordon rings

We prove existence results for travelling waves in discrete, damped, dc-driven sine-Gordon equations with periodic boundary conditions.

$π$-kinks in strongly ac driven sine-Gordon systems

We demonstrate that $π$-kinks exist in non-parametrically ac driven sine-Gordon systems if the ac drive is sufficiently fast. It is found that, at a critical value of the drive amplitude, there are two stable and two unstable equilibria in the sine-Gordon phase. The pairwise symmetry of these equilibria implies the existence of a one-parameter family of $π$-kink solutions in the reduced system. In the dissipative case of the ac driven sine-Gordon systems, corresponding to Josephson junctions, the velocity is selected by the balance between the perturbations. The results are derived from a pert…

Classical behavior of deformed sine-Gordon models

In this work we deform the phi^4 model with distinct deformation functions, to propose a diversity of sine-Gordon-like models. We investigate the proposed models and we obtain all the topological solutions they engender. In particular, we introduce non-polynomial potentials which support some exotic two-kink solutions.

Non-Markovian dynamics of the sine-Gordon solitons

The sine-Gordon equation exhibits a gap in its linear spectrum. That gives rise to memory, or non-Markovian, effects in the soliton formation processes. The generalized variational approach is suggested to derive the model equation that governs the solitary wave evolution. The detailed analytical and numerical studies show that the soliton relaxation dynamics exhibits the main specific features of quantum emitters decay processes in photonic band gap materials. In particular, the non-Markovian effects lead to the extremely long-lived oscillations of the sine-Gordon solitons. That results in th…

Kink dynamics in a novel discrete sine-Gordon system

A spatially-discrete sine-Gordon system with some novel features is described. There is a topological or Bogomol'nyi lower bound on the energy of a kink, and an explicit static kink which saturates this bound. There is no Peierls potential barrier, and consequently the motion of a kink is simpler, especially at low speeds. At higher speeds, it radiates and slows down.

Sine-Gordon孤子的流体动力学描述

Fluid Dynamical Description of Sine-Gordon Solitons

本文提出$1+1$维相对论标量场的流体动力学描述，并将其应用于Sine-Gordon孤子，通过对比局部流体量与孤子标准量揭示其动力学特性。

Noncoaxial multivortices in the complex sine-Gordon theory on the plane

We construct explicit multivortex solutions for the complex sine-Gordon equation (the Lund-Regge model) in two Euclidean dimensions. Unlike the previously found (coaxial) multivortices, the new solutions comprise $n$ single vortices placed at arbitrary positions (but confined within a finite part of the plane.) All multivortices, including the single vortex, have an infinite number of parameters. We also show that, in contrast to the coaxial complex sine-Gordon multivortices, the axially-symmetric solutions of the Ginzburg-Landau model (the stationary Gross-Pitaevskii equation) {\it do not} be…