The generalized Fresnel sine integral Sk(x) and its associated functions Sk+(x) Sk?(x) are defined as locally summable on the real line. integrals have huge applications in physics, specially optics electromaghetics. In many diffraction problems plays an important role. this paper calculated commutative neutrix convolutions of with xr, r = 0,1,2,...

Using a field theory generalization of the spinning top motion, we construct nonabelian generalizations of the sine-Gordon theory according to each symmetric spaces. A La-grangian formulation of these generalized sine-Gordon theories is given in terms of a deformed gauged Wess-Zumino-Witten action which also accounts for integrably perturbed coset conformal field theories. As for physical appli...

We investigate the renormalization group theory of generalized multi-vertex sine-Gordon model by employing dimensional regularization method and also Wilson method. The vertex interaction is given $\cos(k_j\cdot \phi)$ where $k_j$ ($j=1,2,\cdots,M$) are momentum vectors $\phi$ an $N$-component scalar field. beta functions calculated for with multi cosine interactions. second-order correction in...

A general approach to arithmetic Fourier transforms is developed. The implementation is based on the concept of killer polynomials and the solution of an arithmetic deconvolution problem pertaining to a generalized Mobius transform. This results in an extension of the Bruns procedure, valid for all prime numbers, and in an AFT that extracts directly the sine coefficients from the Fourier series.

We study stability of a generalized sine-Gordon model with two coupled scalar fields in two dimensions. Topological soliton solutions are found from the first-order equations that solve the equations of motion. The perturbation equations can be cast in terms of a Schrödinger-like operators for fluctuations and their spectra are calculated. PACS numbers: 0.350.-z, 11.10.Ef

Two families of solutions of a generalized non-Abelian Toda lattice are considered. These solutions are expressed in terms of quasideterminants, constructed by means of Darboux and binary Darboux transformations. As an example of the application of these solutions, we consider the 2-periodic reduction to a matrix sine-Gordon equation. In particular, we investigate the interaction properties of ...

A method for describing the quantum kink states in the semi-classical limit of several (1+1)-dimensional field theoretical models is developed. We use the generalized zeta function regularization method to compute the one-loop quantum correction to the masses of the kink in the sine-Gordon and cubic sinh-Gordon models and another two P(φ)2 systems with polynomial self-interactions.