On the applicability of the layered sine-Gordon model for Josephson-coupled high-T_c layered superconductors

We find a mapping of the layered sine-Gordon model to an equivalent gas of topological excitations and determine the long-range interaction potentials of the topological defects. This enables us to make a detailed comparison to the so-called layered vortex gas, which can be obtained from the layered Ginzburg-Landau model. The layered sine-Gordon model has been proposed in the literature as a candidate field-theoretical model for Josephson-coupled high-T_c superconductors, and the implications of our analysis for the applicability of the layered sine-Gordon model to high-T_c superconductors are discussed. We are led to the conjecture that the layered sine--Gordon and the layered vortex gas models belong to different universality classes. The determination of the critical temperature of the layered sine-Gordon model is based on a renormalization-group analysis.Comment: 7 pages, accepted for publication in J. Phys.: Condens. Matte

On non commutative sinh-Gordon Equation

We give a noncommutative extension of sinh-Gordon equation. We generalize a linear system and Lax representation of the sinh-Gordon equation in noncommutative space. This generalization gives a noncommutative version of the sinh-Gordon equation with extra constraints, which can be expressed as global conserved currents.Comment: 7 Page

Fractional Klein-Gordon equation for linear dispersive phenomena: analytical methods and applications

In this paper we discuss some exact results related to the fractional Klein--Gordon equation involving fractional powers of the D'Alembert operator. By means of a space-time transformation, we reduce the fractional Klein--Gordon equation to a fractional hyper-Bessel-type equation. We find an exact analytic solution by using the McBride theory of fractional powers of hyper-Bessel operators. A discussion of these results within the framework of linear dispersive wave equations is provided. We also present exact solutions of the fractional Klein-Gordon equation in the higher dimensional cases. Finally, we suggest a method of finding travelling wave solutions of the nonlinear fractional Klein-Gordon equation with power law nonlinearities

On the Klein-Gordon equation and hyperbolic pseudoanalytic function theory

Elliptic pseudoanalytic function theory was considered independently by Bers and Vekua decades ago. In this paper we develop a hyperbolic analogue of pseudoanalytic function theory using the algebra of hyperbolic numbers. We consider the Klein-Gordon equation with a potential. With the aid of one particular solution we factorize the Klein-Gordon operator in terms of two Vekua-type operators. We show that real parts of the solutions of one of these Vekua-type operators are solutions of the considered Klein-Gordon equation. Using hyperbolic pseudoanalytic function theory, we then obtain explicit construction of infinite systems of solutions of the Klein-Gordon equation with potential. Finally, we give some examples of application of the proposed procedure

Quantization of Solitons and the Restricted Sine-Gordon Model

We show how to compute form factors, matrix elements of local fields, in the restricted sine-Gordon model, at the reflectionless points, by quantizing solitons. We introduce (quantum) separated variables in which the Hamiltonians are expressed in terms of (quantum) tau-functions. We explicitly describe the soliton wave functions, and we explain how the restriction is related to an unusual hermitian structure. We also present a semi-classical analysis which enlightens the fact that the restricted sine-Gordon model corresponds to an analytical continuation of the sine-Gordon model, intermediate between sine-Gordon and KdV.Comment: 29 pages, Latex, minor updatin