Related papers: Coupled Sine-Gordon and $\phi^4$ System
We study the $\lambda\phi^4_{1+1}$ kink solion and the zero-mode contribution to the Kink soliton mass in regions beyond the semiclassical regime. The calculations are done in the non-trivial scaling region and where appropriate the results…
In this paper we construct analytical self-dual soliton solutions in (1+1) dimensions for two families of models which can be seen as generalizations of the sine-Gordon system but where the kinetic term is non-canonical. For that purpose we…
We use quantum sine-Gordon model to describe the low energy dynamics of a pair of coupled one-dimensional condensates of interacting atoms. We show that the nontrivial excitation spectrum of the quantum sine-Gordon model, which includes…
We investigate propagation of a kink soliton along inhomogeneous chains with two different constituents, arranged either periodically, aperiodically, or randomly. For the discrete sine-Gordon equation and the Fibonacci and Thue-Morse chains…
We argue that topological compactons (solitons with compact support) may be quite common objects if $k$-fields, i.e., fields with nonstandard kinetic term, are considered, by showing that even for models with well-behaved potentials the…
Initial-boundary value problems for complex sine-Gordon and sine-Gordon equations in a semi--strip are treated. The evolution of the Weyl function and a uniqueness result are obtained for complex sine-Gordon equation. The evolution of the…
The field theory Galilean symmetry, which was introduced in the context of modified gravity, gives a neat way to construct Lorentz-covariant theories of a scalar field, such that the equations of motion contain at most second-order…
We investigate generalizations of the $\phi^4$ and sine-Gordon models, including interactions with Dirac Fermions. We observe new resonance phenomena by taking the fermion back-reaction into account. First, we show that the vibrational mode…
We construct a secular theory of a coplanar system of N-planets not involved in strong mean motion resonances, and which are far from collision zones. Besides the point-to-point Newtonian mutual interactions, we consider the general…
We develop a unified theoretical framework for the anisotropic Kondo model and the boundary sine-Gordon model. They are both boundary integrable quantum field theories with a quantum-group spin at the boundary which takes values,…
The multi-soliton solution of the sine-Gordon equation in the presence of elliptic-function background is derived by the inverse scattering method. The key tool in our formulation is the Lax pair written by $4\times4$ matrix differential…
In this paper, we first use semi-classical methods to study quantum field theoretical aspects of the integrable noncommutative sine-Gordon model proposed in [hep-th/0406065]. In particular, we examine the fluctuations at quadratic order…
Nonlinear wave propagation plays a crucial role in the functioning of many physical and biophysical systems. In the propagation regime, disturbances due to the presence of local external perturbations, such as localised defects or boundary…
We consider the interaction of solitary waves in a model involving the well-known $\phi^4$ Klein-Gordon theory, but now bearing both Laplacian and biharmonic terms with different prefactors. As a result of the competition of the respective…
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…
It is shown that the topological discrete sine-Gordon system introduced by Speight and Ward models the dynamics of an infinite uniform chain of electric dipoles constrained to rotate in a plane containing the chain. Such a chain admits a…
A comprehensive symmetry analysis of the N=1 supersymmetric sine-Gordon equation is performed. Two different forms of the supersymmetric system are considered. We begin by studying a system of partial differential equations corresponding to…
The Fourth order $\phi^4$ model generalizes the classical $\phi^4$ model of quantum field theory, sharing the same kink solution. It is also the dispersive counterpart of the well-known parabolic Cahn-Hilliard equation. Mathematically…
The construction of a nonautonomous mixed mKdV/sine-Gordon model is proposed by employing an infinite dimensional affine Lie algebraic structure within the zero curvature representation. A systematic construction of soliton solutions is…
We consider the existence and stability of solitons in a $\chi^{(2)}$ coupler. Both the fundamental and second harmonics undergo gain in one of the coupler cores and are absorbed in the other one. The gain and losses are balanced creating a…