Related papers: A modified discrete sine-Gordon Model
We explore a variant of the $\phi^6$ model originally proposed in Phys.\ Rev.\ D {\bf 12}, 1606 (1975) as a prototypical, so-called, "bag" model in which domain walls play the role of quarks within hadrons. We examine the steady state of…
Sine-Gordon deformed defects that exhibit unusual phenomenological features on the topological charge are investigated. The possibility of a smooth and continuous transition between topological (non null charge) and non-topological (null…
We formulate and discuss integrable analogue of the sine-Gordon equation on arbitrary time scales. This unification contains the sine-Gordon equation, discrete sine-Gordon equation and the Hirota equation (doubly discrete sine-Gordon…
This paper has two purposes. First we present a new definition of the multivariate Pad\'e approximation, a new fast numerical method. Then numerical solution of the one-dimensional (1D) time-dependent nonlinear Sine-Gordon equation (SGE) is…
In this work we consider model of asymmetric kinks, where the behavior of the solution in one side is different from the other side. Also, the models depend of an integer $n$ and, with the increase of $n$, the constructed kink assumes a…
Among finite solutions of Sine-Gordon Equation with in phase N=1, we find Modular and Landen transformation between \theta representation and directly integrated solutions of breather and kink. Because of these transformations, we can say…
We present a new complex non-stationary particle-like solution of the non-linear Klein-Gordon equation with several spatial variables. The construction is based on reduction to an ordinary differential equation.
A discrete phi^4 system is proposed which preserves the topological lower bound on the kink energy. Existence of static kink solutions saturating this lower bound and occupying any position relative to the lattice is proved. Consequently,…
We study the kink motion for the one-dimensional stochastic Allen-Cahn equation and its mass conserving counterpart. Using a deterministic slow manifold, in the sharp interface limit for sufficiently small noise strength we derive an…
A first order equation for a static ${\phi}^4$ kink in the presence of an impurity is extended into an iterative scheme. At the first iteration, the solution is the standard kink, but at the second iteration the kink impurity generates a…
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…
In this article one will discuss the system of coupled nonlinear Klein-Gordon equations with different velocities and different masses. The nonlinearity considered is a general quadratic nonlinearity without any restriction. The method is a…
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…
To show that steadily propagating nonlinear waves in active matter can be driven internally, we develop a prototypical model of a topological kink moving with a constant supersonic speed. We use a model of a bi-stable mass-spring (FPU)…
In this paper we develop a procedure to compute the one-loop quantum correction to the kink masses in generic (1+1)-dimensional one-component scalar field theoretical models. The procedure uses the generalized zeta function regularization…
We analyse several physical aspects of the dressed elliptic strings propagating on $\mathbb{R} \times \mathrm{S}^2$ and of their counterparts in the Pohlmeyer reduced theory, i.e. the sine-Gordon equation. The solutions are divided into two…
We examine various recently proposed discretizations of the well-known $\phi^4$ field theory. We compare and contrast the properties of their fundamental solutions including the nature of their kink-type solitary waves and the spectral…
We study general semilinear scalar-field equations on the real line with variable coefficients in the linear terms. These coefficients are uniformly small, but slowly decaying, perturbations of a constant-coefficient operator. We are…
The d-dimensional n-spin facilitated kinetic Ising model is studied analytically starting from usual master equations and their transformation into a Fock-space representation. The evolution of relevant operators is rewritten in terms of a…
We prove the asymptotic stability of standing kink for the nonlinear relativistic wave equations of the Ginzburg-Landau type in one space dimension: for any odd initial condition in a small neighborhood of the kink, the solution,…