Related papers: Non linear evolution: revisiting the solution in t…
In order to study such effects like parton saturation in final states at the LHC one of the approaches is to combine physics of the BK and the CCFM evolution equations. We report on recently obtained resummed form of the BK equation and…
We propose a general method to study the solutions to nonlinear QCD evolution equations, based on a deep analogy with the physics of traveling waves. In particular, we show that the transition to the saturation regime of high energy QCD is…
The Balitsky-Kovchegov (BK) evolution equation is an equation derived from perturbative Quantum Chromodynamics that allows one to evolve with collision energy the scattering amplitude of a pair of quark and antiquark off a hadron target,…
The Boltzmann equation is studied without the cutoff assumption. Under a perturbative setting, a unique global solution of the Cauchy problem of the equation is established in a critical Chemin-Lerner space. In order to analyse the…
We outline a general method for obtaining the solution to the ($t=0$) BFKL equation in the presence of transverse momentum cutoffs. A lower cutoff allows one to avoid integration over nonperturbative momenta and an upper one is needed from…
We show that solutions of nonlinear nonlocal Fokker--Planck equations in a bounded domain with no-flux boundary conditions can be approximated by Cauchy problems with increasingly strong confining potentials defined in the whole space. Two…
We show how it is possible to rewrite the BFKL equation for the unintegrated gluon distribution, in terms of integrated gluons, similar to that used in DGLAP. We add to our equation the next-to-leading log terms which provide exact…
In the paper we suggest the homotopy method for solving of the non linear evolution equation. This method consists of two steps. First is the analytical solution for the linearized version of the non-linear evolution deep in the saturation…
We explore the subleading-N_c corrections to the large-N_c Balitsky-Kovchegov (BK) evolution equation by comparing its solution to that of the all-N_c Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) equation. In earlier…
We derive generalization of the Balitsky-Kovchegov (BK) equation for a dipole, which consists of a parton and an antiparton of arbitrary charge. At first, we develop one method of indexless transformation of color expressions. The method is…
The generalization of the BFKL equation for the case of non-forward scattering is considered. The kernel of the generalized equation in the next-to-leading approximation is expressed in terms of the gluon Regge trajectory and the effective…
We prove the existence of global renormalized solutions to the Boltzmann equation in bounded domain with incoming boundary condition, with non-cutoff collision kernels. Thus we extend the results of \cite{villani2002noncutoff} for whole…
The main question, that we answer in this paper, is whether the initial condition can influence on the geometric scaling behavior of the amplitude for DIS at high energy. We re-write the non-linear Balitsky-Kovchegov equation in the form…
A large class of physically important nonlinear and nonhomogeneous evolution problems, characterized by advection-like and diffusion-like processes, can be usefully studied by a time-differential form of Kolmogorov's solution of the…
We construct a unique global solution to the Cauchy problem of the 3D Boltzmann equation for initial data around the Maxwellian in the spatially critical homogeneous Besov space…
A fully non-linear kinetic Boltzmann equation for anyons and large initial data is studied in a periodic 1d setting. Strong L1 solutions are obtained for the Cauchy problem. The main results concern global existence, uniqueness, and…
We solve the BFKL equation in the leading logarithmic approximation numerically in the Yang-Mills theory with the Higgs mechanism for the vector boson mass generation. It can be considered as a model for the amplitude with the correct…
We prove existence of a probability solution to the nonlinear stationary Fokker-Planck-Kolmogorov equation on an infinite dimensional space with a centered Gaussian measure $\gamma$ with a unit diffusion operator and a drift of the form…
In the present work, we establish space Bounded Variation $(BV)$ regularity of the solution for a non-linear parabolic partial differential equations involving a linear drift term. We study the problem in a bounded domain with mixed…
We derive the solution of the NLO BFKL equation by constructing its eigenfunctions perturbatively, using an expansion around the LO BFKL (conformal) eigenfunctions. This method can be used to construct a solution of the BFKL equation with…