Related papers: On a modified Vakhnenko-Parkes equation
In this paper we investigate gauged Wess-Zumino-Witten models for space-time groups as gravitational theories, following the trend of recent work by Anabalon, Willison and Zanelli. We discuss the field equations in any dimension and study…
Correlation functions of primary fields in the Wess-Zumino-Novikov-Witten (WZNW) model are known to satisfy a system of Knizhnik-Zamolodchikov (KZ) equations, which involve constants of motion of the exactly-solvable Gaudin magnet. We…
We study spacetimes that lead to a separable Klein-Gordon equation in a general dimension. We introduce an ansatz for the metric in higher dimensions motivated by analogical work by Carter in four dimensions and find solutions of the…
A new way for finding analytical solutions of the three-dimensional sine-Gordon equation is presented. The method is based on the established relation between the solutions of the three-dimensional wave equation and solutions of the…
The sine-Gordon equation is a nonlinear partial differential equation. It is known that the sine-Gordon has soliton solutions in the 1D and 2D cases, but such solutions are not known to exist in the 3D case. Several numerical solutions to…
We develop a theory of the Klein-Gordon equation on curved spacetimes. Our main tool is the method of (non-autonomous) evolution equations on Hilbert spaces. This approach allows us to treat low regularity of the metric, of the…
We present a new complex non-stationary particle-like solution of the non-linear Klein-Gordon equation with several spatial variables. The construction is based on reduction to an ordinary differential equation.
In this paper we continue the program, initiated in Ref. hep-th/0112246, to investigate an integrable noncommutative version of the sine-Gordon model. We discuss the origin of the extra constraint which the field function has to satisfy in…
We prove new integral formulas for generalized hypergeometric functions and their confuent variants. We apply them, via stationary phase formula, to study WKB expansions of solutions: for large argument in the confuent case and for large…
We consider a modified Brans-Dicke theory in which except the usual Brans-Dicke parameter a new dimensionful parameter appears which modifies the kinetic term of the scalar field coupled to gravity. Solving the coupled Einstein-Klein-Gordon…
We prove a new inequality for Gaussian processes, this inequality implies the Gordon-Chevet inequality. Some remarks on Gaussian proofs of Dvoretzky's theorem are given.
Using a simple ansatz for the solutions of the three dimensional generalization of the sine--Gordon and Toda model introduced by Konopelchenko and Rogers, a class of solutions is found by elementary methods. It is also shown that these…
A short review is given of the idea and of the present status of recently proposed evolution equations that respect the Gribov-Lipatov reciprocity between space-like and time-like parton dynamics in all orders.
We investigate solutions of the Klein-Gordon equation in a class of five dimensional geometries presenting the same symmetries and asymptotic structure as the Gross-Perry-Sorkin monopole solution. Apart from globally regular metrics, we…
We propose a procedure for computing the direct scattering transform of the periodic sine-Gordon equation. This procedure, previously used within the periodic Korteweg-de Vries equation framework, is implemented for the case of the…
In this paper, we apply the method of approximate transformation groups proposed by Baikov, Gaziziv and Ibragimov, to compute the first-order approximate symmetry for the Gardner equations with the small parameters. We compute the optimal…
The characteristic representation, or Goursat problem, for the Klein-Fock-Gordon equation with Volkov interaction [1] is regarded. It is shown that in this representation the explicit form of the Volkov propagator can be obtained. Using the…
We consider the deformation of the Whitham system for the non-linear Klein-Gordon equation having the Lorentz-invariant form. Using the Lagrangian formalism of the initial system we obtain the first non-trivial correction to the Whitham…
It is shown how the complex sine-Gordon equation arises as a symmetry flow of the AKNS hierarchy. The AKNS hierarchy is extended by the ``negative'' symmetry flows forming the Borel loop algebra. The complex sine-Gordon and the vector…
We construct the causal (forward/backward) propagators for the massive Klein-Gordon equation perturbed by a first order operator which decays in space but not necessarily in time. In particular, we obtain global estimates for…