Related papers: The evolution of spectral data for nonlinear Klein…
We consider the sine-Gordon equation on metric graphs with simple topologies and derive vertex boundary conditions from the fundamental conservation laws, such as energy and current conservation. Traveling wave solutions for star and tree…
We introduce a new family of integrable theories with $N$ bosons and $N$ freely adjustable mass parameters. These theories restrict in particular limits to the ``generalized supersymmetric'' sine-Gordon models, as well as to the flavor…
We study the properties of the double-frequency sine--Gordon model in the vicinity of the Ising quantum phase transition displayed by this model. Using a mapping onto a generalised lattice quantum Ashkin-Teller model, we obtain critical and…
We extend the theory of non-thermal fixed points to the case of anomalously slow universal scaling dynamics according to the sine-Gordon model. This entails the derivation of a kinetic equation for the momentum occupancy of the scalar field…
The scattering problem for the Klein-Gordon equation with cubic convolution nonlinearity is considered. Based on the Strichartz estimates for the inhomogeneous Klein-Gordon equation we prove the existence of the scattering operator.
The two-frequency sine-Gordon model is examined. The focus is mainly on the case when the ratio of the frequencies is 1/2, given the recent interest in the literature. We discuss the model both in a perturbative (form factor perturbation…
We define and study certain integrable lattice models with non-compact quantum group symmetry (the modular double of U_q(sl_2)) including an integrable lattice regularization of the sinh-Gordon model and a non-compact version of the XXZ…
Quantum dynamics of a collection of atoms subjected to phase modulation has been carefully revisited. We present an exact analysis of the evolution of a two-level system (represented by a spinor) under the action of a time-dependent matrix…
We study integrable deformations of sine-Liouville conformal field theory. Every integrable perturbation of this model is related to the series of quantum integrals of motion (hierarchy). We construct the factorized scattering matrices for…
We address the issue of internal modes of a kink of a discrete sine-Gordon equation. The main point of the present study is to elucidate how the antisymmetric internal mode frequency dependence enters the quasicontinuum spectrum of…
We study linear Klein-Gordon equations with moving potentials motivated by the stability analysis of traveling waves and multi-solitons. In this paper, Strichartz estimates, local energy decay and the scattering theory for these models are…
In this paper we consider the real-valued mass-critical nonlinear Klein-Gordon equations in three and higher dimensions. We prove the dichotomy between scattering and blow-up below the ground state energy in the focusing case, and the…
In the present Chapter, we consider two prototypical Klein-Gordon models: the integrable sine-Gordon equation and the non-integrable $\phi^4$ model. We focus, in particular, on two of their prototypical solutions, namely the kink-like…
In additional to the parity ($\mathcal{P}$) symmetric, time reversal ($\mathcal{T}$) symmetric, and $\mathcal{PT}$ symmetric nonlocal integrable systems, some other types of nonlocal integrable Klein-Gordon models with the space-time…
We consider the problem of scattering for the long range critical nonlinear Klein-Gordon in one space dimension.
We investigate a novel mapping between solutions to several members of the Klein-Gordon family of equations and solutions to equations describing their reductions via the slowly varying envelope approximation. This mapping creates a link…
We investigate the nonlinear stability of global Anti-de Sitter space in the presence of multitrace deformations utilizing an Einstein-Klein-Gordon system with a top-down scalar potential. Our numerical simulations show that marginal and…
We study the effect of discrete symmetry breaking in inhomogeneous scattering media within the framework of generic wave propagation. Our focus is on one-dimensional scattering potentials exhibiting local symmetries. We find a class of…
In the previous work, we classified the solutions to a family of systems of Klein-Gordon equations with non-negative energy below the ground state into two parts: one blows up in finite time while the other extends to a global solution. In…
Some aspects of integrable field theories possessing purely transmitting defects are described. The main example is the sine-Gordon model and several striking features of a classical field theory containing one or more defects are pointed…