相关论文: Solving the Balitsky-Kovchegov equation at next to…
In this paper we study the description of saturation in Balitsky, Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov and Kovner (B-JIMWLK) picture when restricted to observables made up only from dipole operators. We derive a functional…
The aim of this paper is to develop and analyze high-order time stepping schemes for solving semilinear subdiffusion equations. We apply the $k$-step BDF convolution quadrature to discretize the time-fractional derivative with order…
The Gross-Pitaevskii equation with a local cubic nonlinearity that describes a many-dimensional system in an external field is considered in the framework of the complex WKB-Maslov method. Analytic asymptotic solutions are constructed in…
The Higgs boson production associated with a $W$-boson and a photon at the Large Hadron Collider (LHC) can be used to probe the coupling between Higgs boson and vector gauge bosons and discover a signature of new physics. We present the…
We report on recent progress in the evaluation of next-to-leading order (NLO) observables using Lipatov's QCD high energy effective action. We calculate both real and virtual corrections to the quark induced forward jet vertex at NLO,…
A recent type of B-spline functions, namely trigonometric cubic B-splines, are adapted to the collocation method for the numerical solutions of the Kuramoto-Sivashinsky equation. Having only first and second order derivatives of the…
In this paper, we study nonconvex constrained optimization problems with both equality and inequality constraints, covering deterministic and stochastic settings. We propose a novel first-order algorithm framework that employs a…
The initial value problem for an evolution equation of type $v' + Av + BKv = f$ is studied, where $A:V_A \to V_A'$ is a monotone, coercive operator and where $B:V_B \to V_B'$ induces an inner product. The Banach space $V_A$ is not required…
We consider the Cauchy problem for the Gross-Pitaevskii (GP) equation. Using the DBAR generalization of the nonlinear steepest descent method of Deift and Zhou we derive the leading order approximation to the solution of the GP in the…
We consider the singular limit problem in a real Hilbert space for abstract second order evolution equations with a parameter $\varepsilon \in (0,1]$. We first give an alternative proof of the celebrated results due to Kisynski (1963) from…
We consider the next-to-leading order (NLO) calculation of single inclusive particle production at forward rapidities in proton-nucleus collisions and in the framework of the Color Glass Condensate (CGC). We focus on the quark channel and…
Stable computational algorithms for the approximate solution of the Cauchy problem for nonstationary problems are based on implicit time approximations. Computational costs for boundary value problems for systems of coupled multidimensional…
Within the Color Glass Condensate effective theory, we reconsider the next-to-leading order (NLO) calculation of the single inclusive particle production at forward rapidities in proton-nucleus collisions at high energy. Focusing on quark…
We investigate the well-posedness of a class of stochastic second-order in time damped evolution equations in Hilbert spaces, subject to the constraint that the solution lie within the unitary sphere. Then, we focus on a specific example,…
We develop numerical methods for solving the spin-2 Gross-Pitaevskii equation. The basis of our work is a two-way splitting of this evolution equation that leads to two exactly solvable subsystems. Utilizing second-order and fourth-order…
We consider the perturbative description of saturation based on the nonlinear QCD evolution equation of Balitsky and Kovchegov (BK). Although the nonlinear corrections lead to saturation of the scattering amplitude locally in impact…
High energy scattering is considered within the framework of the QCD dipole model formulated as a classical branching process. Starting from Mueller's generating functional we derive the high energy evolution law for the scattering…
We study the the nonlinear Klein-Gordon (NLKG) equation on a manifold $M$ in the nonrelativistic limit, namely as the speed of light $c$ tends to infinity. In particular, we consider an order-$r$ normalized approximation of NLKG (which…
High parton density effects with energy obey non-linear QCD evolution equations for which exact solutions are not known. The mathematical class to which the non-linear Balitsky-Kovchegov equation belongs is identified, proving the existence…
We encode the many-body wavefunction of a Bose-Einstein condensate (BEC) in the $N$-particle sector of an extended catalytic state. This catalytic state is a coherent state for the condensate mode and an arbitrary state for the modes…