Related papers: Rational solutions from Pad\'e approximants for th…
In a typical scenario the diagrammatic many-body perturbation theory generates asymptotic series. Despite non-convergence, the asymptotic expansions are useful when truncated to a finite number of terms. This is the reason for popularity of…
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential…
We discuss some topics concerning rational approximations in Quantum Chromodynamics, especially those related with the mathematical theory of Pad\'e Approximants. We focus on two kind of problems: the first one related with meromorphic…
New travelling wave solutions to the Fornberg-Whitham equation are investigated. They are characterized by two parameters. The expresssions for the periodic and solitary wave solutions are obtained.
We consider a semiclassical approximation for the time evolution of an originally gaussian wave packet in terms of complex trajectories. We also derive additional approximations replacing the complex trajectories by real ones. These yield…
We present a new method for approximating real-valued functions on ${\mathbb R}^+$ by linear combinations of exponential functions with complex coefficients. The approach is based on a multi-point Pad\'e approximation of the Laplace…
A new method to represent and approximate rotation matrices is introduced. The method represents approximations of a rotation matrix $Q$ with linearithmic complexity, i.e. with $\frac{1}{2}n\lg(n)$ rotations over pairs of coordinates,…
The generalized sine-Gordon (sG) equation was derived as an integrable generalization of the sG equation. In this paper, we develop a direct method for solving the generalized sG equation without recourse to the inverse scattering method.…
We give integral formulas to approximate solutions of Dirichlet and Neumann problems for Helmholtz equation at high frequencies. These approximations are valid in the complementary of a union of convex compact obstacles. The first step of…
We consider a generalised Webster's equation for describing wave propagation in curved tubular structures such as variable diameter acoustic wave guides. Webster's equation in generalised form has been rigorously derived in a previous…
We apply the technique of self-similar exponential approximants based on successive truncations of continued exponentials to reconstruct functional laws of the quasi-exponential class from the knowledge of only a few terms of their power…
Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of an operator where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several…
This paper focuses on how to approximate traveling wave solutions for various kinds of partial differential equations via artificial neural networks. A traveling wave solution is hard to obtain with traditional numerical methods when the…
We present a new efficient analytical approximation scheme to two-point boundary value problems of ordinary differential equations (ODEs) adapted to the study of the derivative expansion of the exact renormalization group equations. It is…
Complicated physical problems usually are solved by resorting to perturbation theory leading to solutions in the form of asymptotic series in powers of small parameters. However, finite, and even large values of the parameters often are of…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
Jacobian elliptic travelling wave solutions for a new Hamiltonian amplitude equation determining some instabilities of modulated wave train are obtained. By mere variation of the Jacobian elliptic parameter $k^2$ from zero to one, these…
A new highly efficient method is developed for computation of traveling periodic waves (Stokes waves) on the free surface of deep water. A convergence of numerical approximation is determined by the complex singularites above the free…
The Teukolsky Master Equation is the basic tool for study of perturbations of the Kerr metric in linear approximation. It admits separation of variables, thus yielding the Teukolsky Radial Equation and the Teukolsky Angular Equation. We…
We propose a practical method to solve the random-phase approximation (RPA) in the self-consistent Hartree-Fock (HF) and density-functional theory. The method is based on numerical evaluation of the residual interactions utilizing finite…