Related papers: On $\tau$-function of the quadrilateral lattice
We propose a nonperturbative formulation of chiral gauge theories. The method involves a `pre-regulation' of the gauge fields, which may be implemented on a lattice, followed by a computation of the chiral fermion determinant in the form of…
We discuss how lattice calculations can be a useful tool for the study of structure functions. Particular emphasis is given to the perturbative renormalization of the operators.
We have initiated a program to compute the Compton amplitude from lattice QCD with the Feynman-Hellman method. This amplitude is related to the structure function via a Fredholm integral equation of the first kind. It is known that these…
We revisit the computation of (2-modified) Fredholm determinants for operators with matrix-valued semi-separable integral kernels. The latter occur, for instance, in the form of Green's functions associated with closed ordinary differential…
The thesis deals with applications of fractional calculus to fractals. It introduces the notion of local fractional derivative (LFD). Fractal and multifractal functions have been studied in the thesis using LFD. New kind of equations are…
We have developed a physically-intuitive method to calculate the local lattice constant as a function of position in a high-resolution transmission electron microscopy image by performing a two-dimensional fast Fourier transform. We apply a…
We consider soliton gas solutions of the Focusing Nonlinear Schr\"odinger (NLS) equation, where the point spectrum of the Zakharov-Shabat linear operator condensate in a bounded domain $\mathcal{D}$ in the upper half-plane. We show that the…
The Hamiltonian approach to the theory of dual isomonodromic deformations is developed within the framework of rational classical R-matrix structures on loop algebras. Particular solutions to the isomonodromic deformation equations…
We consider a nonlinear parabolic equation of fractional order in space and propose its numerical discretization. The fractional derivative is defined through a functional analytic setting, rather than the traditional definition of…
In the present paper we discuss the general facts, concerning the Schlesinger system: the (\tau)-function, the local factorization of solutions of Fuchsian equations and holomorphic deformations. We introduce the terminology "isoprincipal"…
We study the effects of adding a local perturbation in a pattern forming system, taking as an example the Ginzburg-Landau equation with a small localized inhomogeneity in two dimensions. Measuring the response through the linearization at a…
We survey methods and results of fractional differential equations in which an unknown function is under the operation of integration and/or differentiation of fractional order. As an illustrative example, we review results on fractional…
By means of partial fraction method, we investigate the decomposition of rational functions. Several striking identities on harmonic numbers and generalized Apery numbers will be established, including the binomial-harmonic number identity…
In this paper, we propose a solution of fractional logistic equation by using properties of Mittag-Leffler function.
In this paper, we study the fourth-order Schr\"{o}dinger equation \begin{equation*} i \partial_t u + {\Delta}^2 u - \gamma \Delta u = \pm |u|^{s-1}u \end{equation*} on the lattice $\mathbb{Z}^d$ with dimensions $d=1,2$ and parameter $\gamma…
We consider the dynamical correlation functions of the quantum Nonlinear Schrodinger equation. In a previous paper we found that the dynamical correlation functions can be described by the vacuum expectation value of an operator-valued…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
Matrix integrals used in random matrix theory for the study of eigenvalues of matrix ensembles have been shown to provide $ \tau $-functions for several hierarchies of integrable equations. In this paper, we construct the matrix integral…
We introduce a new numerical method, based on Bernoulli polynomials, for solving multiterm variable-order fractional differential equations. The variable-order fractional derivative was considered in the Caputo sense, while the…
We prove integrability of a generalised non-commutative fourth order quintic nonlinear Schrodinger equation. The proof is relatively succinct and rooted in the linearisation method pioneered by Ch. Poppe. It is based on solving the…