Related papers: The evolution of spectral data for nonlinear Klein…
We consider deformations of the $SU(3)$ Affine Toda theory (AT) and investigate the integrability properties of the deformed theories. We find that for some special deformations all conserved quantities change to being conserved only…
Effective mass Klein-Gordon equation for the asymmetric Hulth{\'e}n potential is solved in terms of hypergeometric functions. Results are obtained for the scattering and bound states with the position dependent mass and constant mass, as a…
We solve the Klein-Gordon equation in the presence of a spatially one-dimensional Woods-Saxon potential. The scattering solutions are obtained in terms of hypergeometric functions and the condition for the existence of transmission…
We study different aspects of integrable boundary quantum field theories, focusing mostly on the ``boundary sine-Gordon model'' and its applications to condensed matter physics. The first part of the review deals with formal problems. We…
As shown in [hep-th/0406065], there exists a noncommutative deformation of the sine-Gordon model which remains (classically) integrable but features a second scalar field. We employ the dressing method (adapted to the Moyal-deformed…
We construct a modified non-BPS sine-Gordon theory which supports stable static kinks of arbitrary topological degree $N$. We use this toy model to study problems which are interesting for higher-dimensional soliton theories supporting…
On a Riemannian manifold with or without boundary, and whether bounded or unbounded, we consider a semilinear wave (or Klein-Gordon) equation with a subcritical nonlinearity (either defocusing or focusing). We establish local…
In this paper we describe the integral transform that allows to write solutions of one partial differential equation via solution of another one. This transform was suggested by the author in the case when the last equation is a wave…
In this work we investigate the validity limits of the modulational approximation as a method to describe the nonlinear interaction of conservative wave fields. We focus on a nonlinear Klein-Gordon equation and suggest that the breakdown of…
We study the convergence of solutions of the discrete nonlinear Klein-Gordon equation on an infinite lattice in the continuum limit, using recent tools developed in the context of nonlinear discrete dispersive equations. Our approach relies…
A class of decoherence schemes is described for implementing the principles of generalized quantum theory in reparametrization-invariant `hyperbolic' models such as minisuperspace quantum cosmology. The connection with sum-over-histories…
We study the coupled wave-Klein-Gordon systems, introduced by LeFloch-Ma and then Ionescu-Pausader, to model the nonlinear effects from the Einstein-Klein-Gordon equation in harmonic coordinates. We first go over a slightly simplified…
We establish the isomorphism between a nonlinear $\sigma$-model and the abelian gauge theory on an arbitrary curved background, which allows us to derive integrable models and the corresponding Lax representations from gauge theoretical…
We establish the isomorphism between a nonlinear $\sigma$-model and the abelian gauge theory on an arbitrary curved background, which allows us to derive integrable models and the corresponding Lax representations from gauge theoretical…
The subject of this thesis is the rigorous construction of QFT models with nontrivial interaction. Two different approaches in the framework of AQFT are discussed. On the one hand, an inverse scattering problem is considered. A given…
We derive approximate expressions for the dispersion relation of the nonlinear Klein-Gordon equation in the case of strong nonlinearities using a method based on the Linear Delta Expansion. All the results obtained in this article are fully…
Recently, it has been shown that the generalized symmetric Woods-Saxon potential energy, in which surface interaction terms are taken into account, describes the physical processes better than the standard form. Therefore in this study, we…
We review applications of the sine-Gordon model, the O(3) non-linear sigma model, the U(1) Thirring model, and the O(N) Gross--Neveu model to quasi one-dimensional quantum magnets, Mott insulators, and carbon nanotubes. We focus upon the…
The Riemann-Hilbert problem associated with the integrable PDE is used as a nonlinear transformation of the nearly integrable PDE to the spectral space. The temporal evolution of the spectral data is derived with account for arbitrary…
In this paper we study the phenomenon of nonlinear supratransmission in a semi-infinite discrete chain of coupled oscillators described by modified sine-Gordon equations with constant external and internal damping, and subject to harmonic…