Related papers: An alternative scaling solution for high-energy QC…
We introduce an alternative to the method of matched asymptotic expansions. In the "traditional" implementation, approximate solutions, valid in different (but overlapping) regions are matched by using "intermediate" variables. Here we…
In this paper we calculate dipole amplitude and dipole amplitude correlations using first and second equation from Balitsky-Kovchegov hierarchy. Our analysis shows that even in presence of weak dipole correlation in initial condition mean…
By a bifurcation argument we prove that the capillary-gravity Whitham equation features asymmetrical periodic travelling wave solution of arbitrarily small amplitude. Such waves exist only in the weak surface tension regime…
We consider the scaling similarity solutions of two integrable cubically nonlinear partial differential equations (PDEs) that admit peaked soliton (peakon) solutions, namely the modified Camassa-Holm (mCH) equation and Novikov's equation.…
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…
A nonperturbative model for the QCD invariant charge, which contains no low-energy unphysical singularities and possesses an elevated higher loop corrections stability, is developed in the framework of potential approach. The static…
We study the existence, regularity, and symmetry of periodic traveling solutions to a class of Gardner-Ostrovsky type equations, including the classical Gardner-Ostrovsky equation, the (modified) Ostrovsky, and the reduced (modified)…
The numerical solutions of the non-linear evolution equation are shown to display the ``geometric'' scaling recently discovered in the experimental data. The phenomena hold both for proton and nucleus targets for all $x$ below $10^{-2}$ and…
In this paper we study the global existence of small data solutions to the Cauchy problem for the semilinear wave equation with scale-invariant damping. We obtain estimates for the solution and its energy with the same decay rate of the…
A new approach to high energy evolution based on a linear equation for QCD generating functional is developed. This approach opens a possibility for systematic study of correlations inside targets, and, in particular, inside realistic…
New types of stationary solutions of a one-dimensional driven sixth-order Cahn-Hilliard type equation that arises as a model for epitaxially growing nano-structures such as quantum dots, are derived by an extension of the method of matched…
We prove the existence of a family of travelling wave solutions in a variant of the $\textit{Zeldovich-Frank-Kamenetskii (ZFK) equation}$, a reaction-diffusion equation which models the propagation of planar laminar premixed flames in…
Using the ``Quality Factor'' (QF) method, we analyse the scaling properties of deep-inelastic processes at HERA and fixed target experiments for x<0.01. We look for scaling formulae of the form sigma(tau), where tau(log Q^2, Y) is a scaling…
The Balitsky-Kovchegov equation describes the high-energy growth of gauge theory scattering amplitudes as well as nonlinear saturation effects which stop it. We obtain the three-loop corrections to this equation in planar $\mathcal{N}=4$…
In this paper, we use the variational method, especially the perturbation method, to find the perturbed high energy solutions of the quadratic coupled Schrodinger system with asymmetric asymptotic potential and their asymptotic behavior as…
We establish the dual notions of scaling and saturation from geometric control theory in an infinite-dimensional setting. This generalization is applied to the low-mode control problem in a number of concrete nonlinear partial differential…
As is known from QED, a possible solution to the ghost-pole trouble can be obtained by imposing the $Q^2$-analyticity imperative. Here, the pole is compensated by the $\alpha$ non-analytic contribution that results in finite coupling…
The new model for the QCD analytic running coupling, proposed recently, is extended to the timelike region. This running coupling naturally arises under unification of the analytic approach to QCD and the renormalization group (RG)…
We show that the Iancu-Mueller factorization has a simple interpretation in the Reggeon - like technique based on the BFKL Pomeron. The formula for calculating the high energy asymptotic behaviour for the colour dipole-dipole amplitude is…
Travelling-wave solutions are shown to bifurcate from relative periodic orbits in plane Poiseuille flow at Re = 2000 in a saddle-node infinite period bifurcation. These solutions consist in self-sustaining sinuous quasi-streamwise streaks…