Related papers: A predictive phenomenological tool at small Bjorke…
``Geometric scaling'', i.e. the dependence of DIS cross-sections on the ratio Q/Q_S, where Q_S(Y) is the rapidity-dependent \saturation scale, can be theoretically obtained from universal ``traveling wave'' solutions of the nonlinear…
In this study, we employ the homogeneous balance method to obtain an analytical solution to the Balitsky-Kovchegov equation with running coupling. We utilize two distinct prescriptions of the running coupling scale, namely the saturation…
Nonlinear QCD evolution equations are essential tools in understanding the saturation of partons at small Bjorken $x_{\rm B}$, as they are supposed to restore an upper bound of unitarity for the cross section of high energy scattering. In…
We show that high energy scattering is a statistical process essentially similar to reaction-diffusion in a system made of a finite number of particles. The Balitsky-JIMWLK equations correspond to the time evolution law for the particle…
Within the framework of the dipole factorisation, we use a recent collinearly-improved version of the Balitsky-Kovchegov equation to fit the HERA data for inclusive deep inelastic scattering at small Bjorken $x$. The equation includes an…
Using consistent truncations of the BFKL kernel, we derive analytical traveling-wave solutions of the Balitsky-Kovchegov saturation equation for both fixed and running coupling. A universal parametrization of the ``interior'' of the wave…
We study global well-posedness for the Kadomtsev-Petviashvili II equation in three space dimensions with small initial data. The crucial points are new bilinear estimates and the definition of the function spaces. As by-product we obtain…
Within the framework of a (1+1)--dimensional model which mimics high energy QCD, we study the behavior of the cross sections for inclusive and diffractive deep inelastic $\gamma^*h$ scattering cross sections. We analyze the cases of both…
Phenomenological models of the dipole cross section that enters in the description of for instance deep inelastic scattering at very high energies have had considerable success in describing the available small-x data in both the saturation…
The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N stochastic variables with Lochner's generalized Dirichlet distribution (R.H. Lochner, A Generalized…
By combining the DiPerna and Lions techniques for the nonrelativistic Boltzmann equation and the Dudy\'{n}ski and Ekiel-Je\.{z}ewska device of the causality of the relativistic Boltzmann equation, it is shown that there exists a global mild…
We present the modified approach to the classical Bogolyubov-Krylov averaging, developed recently for the purpose of PDEs. It allows to treat Lipschitz perturbations of linear systems with pure imaginary spectrum and may be generalized to…
Extending independently the Balitsky-Kovchegov (BK) equation to running coupling or to fluctuation effects due to Pomeron loops is known to lead in both cases to qualitative changes of the traveling-wave asymptotic solutions. In this paper…
An extended collinearly-improved Balitsky-Kovchegov evolution equation in the target rapidity representation is derived by including the running coupling corrections during the expansion of the "real" $S$-matrix. We find that the running…
This paper is dedicated to the global well-posedness issue of the compressible Oldroyd-B model in the whole space $\R^d$ with $d\ge2$. It is shown that this set of equations admits a unique global solution in a certain critical Besov space…
The Balitsky-Kovchegov QCD equation for rapidity evolution describing saturation effects at high energy admits universal asymptotic traveling-wave solutions when the nonlinear damping becomes effective. The asymptotic solutions fall in…
In this paper we present the results of numerical studies of the JIMWLK and BK equations with a particular emphasis on the universal scaling properties and phase space structure involved. The results are valid for near zero impact parameter…
This paper is dedicated to the Cauchy problem of the incompressible Oldroyd-B model with general coupling constant $\om\in (0,1)$. It is shown that this set of equations admits a unique global solution in a certain hybrid Besov spaces for…
It is shown that a generalization of the Painlev\'e-II equation (P-II) to a system of coupled equations with symmetry breaking terms is integrable. A Lax pair for this system is used to relate the asymptotic behavior of the solutions at…
We define a mapping of the QCD Balitsky-Kovchegov equation in the diffusive approximation with noise and a generalized coupling allowing a common treatment of the fixed and running QCD couplings. It corresponds to the extension of the…