Related papers: QCD Saturation Equations including Dipole-Dipole C…
An approximate analytical solution of the Balitsky-Kovchegov (BK) equation using the homotopy perturbation method (HPM) is suggested in this work. We have carried out our work in perturbative QCD (pQCD) dipole picture of deep inelastic…
The nonlinear Balitsky-Kovchegov equation at small x is solved numerically, incorporating impact parameter dependence. Confinement is modeled by including effective gluon mass in the dipole evolution kernel, which regulates the splitting of…
We discuss the high energy diffractive dissociation in DIS at the Next to Leading Order. In the large $N_c$ dipole limit we derive the NLO version of the Kovchegov-Levin equation. We argue that the original structure of the equation is…
In the perturbative QCD with $N_c\to\infty$ the amplitude for the collision of two heavy nuclei is expressed via dipole densities in the nuclei. Coupled equations for these densities are derived in the configuration space. The equations are…
We study the complex Ginzburg-Landau equation posed on possibly unbounded domains, including some singular and saturated nonlinear damping terms. This model interpolates between the nonlinear Schr{\"o}dinger equation and dissipative…
Unintegrated gluon densities in nuclei, dipole-nucleus cross-sections and quark densities are numerically investigated in the high-colour limit, with the scattering on a heavy nucleus exactly described by the sum of fan diagrams of BFKL…
Integrable dispersionless Kadomtsev-Petviashvili (KP) hierarchy of B type is considered. Addition formula for the $\tau$-function and conformally invariant equations for the dispersionless BKP (dBKP) hierarchy are derived. Symmetry…
We consider a simplified version of the Budyko diffusive energy balance climate model. We obtain the exact number of monotone stationary solutions of the associated discontinuous nonlinear elliptic with absorption. We show that the…
How do we describe non-trivial bulk measurements relative to an observer (i.e. relationally) when both the observer and the system it probes may/may not evolve in time? How can we interpret this holographically; particularly for zero-energy…
In a semi-infinite geometry, a 1D, M-component model of biological evolution realizes microscopically an inhomogeneous branching process for $M \to \infty$. This implies in particular a size distribution exponent $\tau'=7/4$ for avalanches…
In this paper spatial correlations of parallel edge dislocations are studied. After closing a hierarchy of equations for the many-particle density functions by the Kirkwood superposition approximation, we derive evolution equations for the…
We present a global fit to HERA data on the reduced cross section measured in electron-proton collisions in the region of small Bjorken-$x$: $x\le x_0=10^{-2}$ and moderate to high values of the virtuality $Q^2<Q^2_{max}=650$ GeV$^2$. The…
In this article, we indicate that under suitable assumptions of a modulus of continuity we obtain either the global (in time) existence of small data Sobolev solutions or the blow-up result of local (in time) Sobolev solutions to…
An eigenvalue problem with a reference function and the corresponding hierarchy of nonlinear evolution equations are proposed. The bi-Hamiltonian structure of the hierarchy is established by using the trace identity. The isospectral problem…
Recently, a two-matrix-model with a new type of interaction [1] has been introduced and analyzed using bi-orthogonal polynomial techniques. Here we present the complete 1/N^2 expansion for the formal version of this model, following the…
Recently Kovner and Lublinsky proposed a set of equations which can be viewed as dual to JIMWLK evolution. We show that these dual equations have a natural dipole-like structure, as conjectured by Kovner and Lublinsky. In the high energy…
We introduce a saturation model for photon-photon interactions, based on a QCD dipole picture of high energy scattering. The two-dipole cross-section is assumed to satisfy the saturation property. This pomeron-like contribution is…
The existence of decomposition solutions of the well-known nonlinear BKP hierarchy is explored. It is shown that these decompositions provide simple and interesting relationships between classical integrable systems and the BKP hierarchy.…
We study a semi-linear version of the Skyrme system due to Adkins and Nappi. The objects in this system are maps from $(1+3)$-dimensional Minkowski space into the $3$-sphere and 1-forms on $\mathbb{R}^{1+3}$, coupled via a Lagrangian…
In this paper, we consider the dynamics of solutions to complex-valued evolutionary partial differential equations (PDEs) and show existence of heteroclinic orbits from nontrivial equilibria to zero via computer-assisted proofs. We also…