In this paper, with the aid of Maple, the (G ′ /G) and (1/G ′ )-expansion methods are applied to determine the exact solutions of (N+1)-dimensional generalized Boussinesq equation and (N+1)-dimensional sine-cosine-Gordon equation.These equations play a very important role in mathematical physics and engineering sciences. This methods are more powerful and will be used in further works to establ...

We examine the two-point correlation functions of the fields exp(iαΦ) in the sine-Gordon theory at all values of the coupling constantˆβ. Using conformal perturbation theory, we write down explicit integral expressions for every order of the short distance expansion. Using a novel technique analagous to dimensional regularisation, we evaluate these integrals for the first few orders finding exp...

The well-known phase structure of the two-dimensional Coulomb-gas was investigated in several papers by using the differential RG approach with a smooth cut-off in the momentum space (or equivalently using a sharp cut-off in the coordinate space) (Kosterlitz 1973, Kosterlitz 1974, Jose 1977, Huang 1991, Gersdorff 2000). Our goal is in this work to determine the RG flow for the two-dimensional C...

We demonstrate that the G ′ /G expansion method which is often used in finding exact solutions of nonlinear differential equation is equivalent to the well – known tanh method and application of these methods gives the same exact solutions of nonlinear differential equations.

We describe and characterize rigorously the chaotic behavior of the sine– Gordon equation. The existence of invariant manifolds and the persistence of homoclinic orbits for a perturbed sine–Gordon equation are established. We apply a geometric method based on Mel’nikov’s analysis to derive conditions for the transversal intersection of invariant manifolds of a hyperbolic point of the perturbed ...

Some properties of the non-commutative versions of the sine-Gordon model (NCSG) and the corresponding massive Thirring theories (NCMT) are studied. Our method relies on the NC extension of integrable models and the master Lagrangian approach to deal with dual theories. The master Lagrangians turn out to be the NC versions of the so-called affine Toda model coupled to matter fields (NCATM) assoc...

It has been argued that for a finite two-dimensional classical Coulomb system of characteristic size R, in its conducting phase, as R → ∞ the total free energy (times the inverse temperature β) admits an expansion of the form: βF = AR +BR+ 1 6 χ lnR, where χ is the Euler characteristic of the manifold where the system lives. The first two terms represent the bulk free energy and the surface fre...

Abstract Exact solutions to nonlinear differential equations play an undeniable role in various branches of science. These are often used as reliable tools describing the quantitative and qualitative features phenomena observed many fields mathematical physics sciences. In this paper, generalized exponential rational function method extended sinh-Gordon equation expansion applied obtain approxi...