Related papers: On a modified Vakhnenko-Parkes equation
It is shown that the alternative Klein-Gordon equation with positive definite probability density proposed in a letter by M.D. Kostin does not meet the requirements of relativistic (quantum) field theory and therefore does not allow for a…
We report on the well-posedness of the Feynman problem for the Klein-Gordon equation on asymptotically Minkowski spacetimes. The main result is the invertibility of the Klein-Gordon operator with Feynman conditions at infinite times.…
This article develops a variational formulation for the relativistic Klein-Gordon equation. The main results are obtained through an extension of the classical mechanics approach to a more general context, which in some sense, includes the…
A peculiar representation of the Lorentz group is suggested as a starting point for a consistent approach to relativistic quantum theory.
By viewing Einstein's field equations -- reduced to two dimensions -- as an integrable system, one can simultaneously obtain exact solutions to both the equations themselves and their associated Lax pair via a canonical Wiener-Hopf…
Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.
We study the dynamics of a modified-gravity theory, which is supplemented by an extended Gibbons-Hawking-York boundary term and incorporates diffeomorphism violation through nondynamical background fields denoted as $u$ and $s^{\mu\nu}$ in…
We study integrable lattice regularizations of the sine-Gordon model with the help of the separation of variables method of Sklyanin and the Baxter Q-operators. This leads us to the complete characterization of the spectrum (eigenvalues and…
Initial-boundary value problem for the modified Zakharov-Kuznetsov equation posed on a bounded rectangle is considered. The main difficulty is the critical power in nonlinear term. The results on existence, uniqueness and asymptotic…
Using the improved lower bound on the sum of the eigenvalues of the Dirichlet Laplacian proved by A. D. Melas (Proc. Amer. Math. Soc. \textbf{131} (2003) 631-636), we report a new and sharp estimate for the dimension of the global attractor…
We find the general solution of the equations of motion for the WZNW system in curved space-time for arbitrary external gauge fields. Using the connection between the WZNW system for $SL(2,R)$ group and 2D induced gravity we obtain the…
We give the governing equations for multiple scalar fields in a flat Friedmann-Robertson-Walker (FRW) background spacetime on all scales, allowing for metric and field perturbations up to second order. We then derive the Klein-Gordon…
We provide detailed arguments on how to derive properties of generalized form factors, originally proposed by one of the authors (M.K.) and Weisz twenty years ago, solely based on the assumption of "minimal analyticity" and the validity of…
We unveil a remarkable connection between the sine-Gordon quantum field theory and the Kardar-Parisi-Zhang (KPZ) growth equation. We find that the non-relativistic limit of the two point correlation function of the sine-Gordon theory is…
Modified gravity provides a possible explanation for the currently observed cosmic accelaration. In this paper, we study general classes of modified gravity models. The Einstein-Hilbert action is modified by using general functions of the…
In this paper, the method of approximate transformation groups which was proposed by Baikov, Gazizov and Ibragimov, is extended on Hamiltonian and bi-Hamiltonian systems of evolution equations. Indeed, as a main consequence, this extended…
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.
This is the third in a sequence of papers in which we construct a quantum version of the Kirwan map from the equivariant quantum cohomology of a smooth polarized complex projective variety with the action of a connected complex reductive…
The effect of modifying General Relativity with the addition of some higher dimensional operators, generalizations of the Goroff-Sagnotti operator, is discussed. We determine in particular, the general solution of the classical equations of…
We present a construction of a Virasoro symmetry of the sine-Gordon (SG) theory. It is a dynamical one and has nothing to do with the space-time Virasoro symmetry of 2D CFT. Although it is clear how it can be realized dyrectly in the SG…