相关论文: Reality problems in the soliton theory
In this note we show that the single soliton solutions known previously in the $1+1$ dimensional affine Toda field theories from a variety of different methods \cite{H1,MM,OTUa,OTUb}, are in fact not the most general single soliton…
Ball lightning is one of the most mysterious atmospheric phenomena, whose long lifetime, penetrative ability, and stability are difficult to explain with traditional physical models. This paper proposes a novel theoretical framework,…
The perturbation theory around the soliton fields of the sin-Gordon model is developed in the coset space. It is shown by explicit calculations that all corrections to the topological soliton contribution are canceled exactly.
We find infinitely many soliton-like solutions in a deformation of the sine-Gordon theory in $(d+1)$-dimensional $AdS_{d+1}$ (anti-de Sitter) spacetime for $d \geq 2$, as well as single solitonic solutions in $dS_{d+1}$ (de Sitter) and…
The scattering of charged solitons in the complex sine-Gordon field theory is investigated. An exact factorizable S-matrix for the theory is proposed when the renormalized coupling constant takes the values $\lambda^{2}_{R}=4\pi/k$ for any…
The forced soliton equation is the starting point for semiclassical computations with solitons away from the small momentum transfer regime. This paper develops necessary analytical and numerical tools for analyzing solutions to the forced…
The so-called conformal affine Toda theory coupled to the matter fields (CATM), associated to the $\hat{sl}(2)$ affine Lie algebra, is studied. The conformal symmetry is fixed by setting a connection to zero, then one defines an…
Potentials arising in ultraviolet-completed field theories can be devoid of singularities, and hence render spacetimes simply connected. This challenges the notion of topological invariants considered in such scenarios. We explore the…
Using the same method we provide negative answers to the following questions: Is it possible to find real equations for complex polynomials in two variables up to topological equivalence (Lee Rudolph) ? Can two topologically equivalent…
Dark and grey soliton-like states are shown to emerge from numerically constructed superpositions of translationally-invariant eigenstates of the interacting Bose gas in a toroidal trap. The exact quantum many-body dynamics reveals a…
The coalescence and disappearance of Hartree--Fock (HF) solutions as the molecular structure varies have been a common source of criticism for the breakdown of the HF approximation to the potential energy surfaces. However, recent…
A systematic method is presented to provide various equivalent solution formulas for exact solutions to the sine-Gordon equation. Such solutions are analytic in the spatial variable $x$ and the temporal variable $t,$ and they are…
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…
An alternative method to the topological instanton solution for deriving an expression for the topological charge is presented. This alternative method involves the use of relativistic quantum field theory and covariant electrodynamics. In…
In the theory of optical gap solitons, slowly-moving finite-amplitude Lorentzian solutions are found to mediate the transition from bright to coexistent dark-antidark solitary wave pairs when the laser frequency is detuned out of the proper…
We present an application of the basic mathematical concept of complex functions as topological solitons, a most interesting area of research in physics. Such application of complex theory is virtually unknown outside the community of…
Unidirectional motion of solitons can take place, although the applied force has zero average in time, when the spatial symmetry is broken by introducing a potential $V(x)$, which consists of periodically repeated cells with each cell…
A model of soliton-defect interactions in the sine-Gordon equations is studied using singular perturbation theory. Melnikov theory is used to derive a critical velocity for strong interactions, which is shown to be exponentially small for…
We consider localized soliton-like solutions in the presence of a stable scalar condensate background. By the analogy with classical mechanics, it can be shown that there may exist solutions of the nonlinear equations of motion that…
We review the construction of a particular soliton-type solution of the classical Einstein and matter-field equations. This localized finite-energy static classical solution can be interpreted as a single spacetime defect embedded in…