Related papers: Classes of Exact Solutions to the Teukolsky Master…
A systematic search for the Lie point symmetries admitted by the steady hydromagnetic two-dimensional incompressible viscous flow boundary layer equation and associated boundary conditions is performed. Unlike previous works, the specific…
Some explicit traveling wave solutions to a Kolmogorov-Petrovskii-Piskunov equation are presented through two ans\"atze. By a Cole-Hopf transformation, this Kolmogorov-Petrovskii-Piskunov equation is also written as a bilinear equation and…
Starting with the whole class of type-D vacuum backgrounds with cosmological constant we show that the separated Teukolsky equation for zero rest-mass fields with spin $s=\pm 2$ (gravitational waves), $s=\pm 1$ (electromagnetic waves) and…
We propose a simple algebraic method for generating classes of traveling wave solutions for a variety of partial differential equations of current interest in nonlinear science. This procedure applies equally well to equations which may or…
The numerical solution of linear discrete ill-posed problems typically requires regularization, i.e., replacement of the available ill-conditioned problem by a nearby better conditioned one. The most popular regularization methods for…
We use Heun type solutions given in \cite{Suzuki} for the radial Teukolsky equation, written in the background metric of the Kerr-Newman-de Sitter geometry, to calculate the quasinormal frequencies for polynomial solutions and the…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
Stochastic master equations are often used to describe conditional spin squeezing of atomic ensemble, but are limited so far to the systems with few atoms due to the exponentially increased Hilbert space. In this article, we present an…
New method is presented to look for exact solutions of nonlinear differential equations. Two basic ideas are at the heart of our approach. One of them is to use the general solutions of the simplest nonlinear differential equations. Another…
This paper is concerned with the solution of large-scale linear discrete ill-posed problems with error-contaminated data. Tikhonov regularization is a popular approach to determine meaningful approximate solutions of such problems. The…
Our goal is to find closed form analytic expressions for the solitary waves of nonlinear nonintegrable partial differential equations. The suitable methods, which can only be nonperturbative, are classified in two classes. In the first…
Wave Kinetic Equations (WKEs) are often used to describe the evolution of ensemble averaged wave amplitudes for nonlinear wave systems. In the present manuscript we describe a new approach to direct numerical simulation of solutions to…
For one-dimensional linear kinetic equations analytical solutions of problems about moderately strong evaporation (condensation), when frequency of collisions of molecules is constant, are received . The equation and distribution function…
The generalized Bretherton equation is studied. The classification of the meromorphic traveling wave solutions for this equation is presented. All possible exact solutions of the generalized Brethenton equation are given.
The Kraus representation of quantum channels allows for a precise emulation of the complex dynamics that take place on quantum processors, whether for benchmarking algorithms, predicting the performance of error correction and mitigation,…
Sampling equation method is presented to look for exact solutions of nonlinear differential equations. Application of this approach to one of the extensive chaos model is considered. Exact solutions of this model in travelling wave are…
Numerical methods for the Euler equations with a singular source are discussed in this paper. The stationary discontinuity induced by the singular source and its coupling with the convection of fluid presents challenges to numerical…
To estimate Kaluza-Klein (KK) corrections on gravitational waves emitted by perturbed rotating black strings, we give the effective Teukolsky equation on the brane which is separable equation and hence numerically manageable.
The fundamental solution of the classical approximation of a three waves kinetic equation that happens in the kinetic theory of a condensed gas of bosons near the critical temperature is obtained. It is also proved to be unique in a…
New method for finding exact solutions of nonlinear differential equations is presented. It is based on constructing the polygon corresponding to the equation studied. The algorithms of power geometry are used. The method is applied for…