Related papers: On the solution to the NLO forward BFKL equation
We apply the GBDT version of the B\"acklund-Darboux transformation to the nonlocal NLS (focusing and defocusing cases). The matrix case is included and solutions in the form of rectangular $m_1 \times m_2$ matrix functions are dealt with.…
This is an extended and pedagogically oriented version of our recent work, in which we proposed an improvement of the splitting functions at small x which overcomes the apparent problems encountered by the BFKL approach.
I review the recent progress in small $x$ physics, concentrating on the topics relevant to the BFKL evolution.
We investigate the diffusion of particles in an attractive one-dimensional potential that grows logarithmically for large $|x|$ using the Fokker-Planck equation. An eigenfunction expansion shows that the Boltzmann equilibrium density does…
We present the full next-to-leading order (NLO) prediction for the jet-gap-jet cross section at the LHC within the BFKL approach. We implement, for the first time, the NLO impact factors in the calculation of the cross section. We provide…
We present the first numerical solution to the next to leading order Balitsky-Kovchegov (BK) equation in coordinate space in the large-$N_\mathrm{c}$ limit. In addition to the dipole operator we also solve the evolution of the "conformal…
In this paper we study some boundary value problems for a fractional analogue of second order elliptic equation with an involution perturbation in a rectangular domain. Theorems on existence and uniqueness of a solution of the considered…
A general solution to the Complex Bateman equation in a space of arbitrary dimensions is constructed.
The general solution to the Complex Bateman equation is constructed. It is given in implicit form in terms of a functional relationship for the unknown function. The known solution of the usual Bateman equation is recovered as a special…
We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order…
The quantum problem of an electron moving in a plane under the field created by two Coulombian centers admits simple analytical solutions for some particular inter-center distances. These elementary eigenfunctions, akin to those found by…
In this paper, we consider the planar forced N-pendulum equation. Multiple rotational solutions are obtained.
The inversion theorem and convolution theorem of the conformable fractional Laplace transforms are developed. All the elementary properties of the classical Laplace transform are extended to the conformable fractional transform, and using…
We extend bifurcation results of nonlinear eigenvalue problems from real Banach spaces to any neighbourhood of a given point. For points of odd multiplicity on these restricted domains, we establish that the component of solutions through…
We prove some bounds for the eigenfunctions of the Stokes problem under Navier boundary conditions in a cube.
Lanford has shown that Feigenbaum's functional equation has an analytic solution. We show that this solution is a polynomial time computable function. This implies in particular that the so-called first Feigenbaum constant is a polynomial…
The production of forward jets of transverse momentum $p_T(j)\approx Q$ and large momentum fraction $x_{jet}\gg x$ probes the onset of BFKL dynamics at HERA. A full ${\cal O}(\alpha_s^2)$ calculation of the inclusive forward jet cross…
A representation formula for solutions of stochastic partial differential equations with Dirichlet boundary conditions is proved. The scope of our setting is wide enough to cover the general situation when the backward characteristics that…
We analytically solve for the time dependent solutions of various density evolution models. With specific forms of the diffusion, drift and sink coefficients, the eigenfunctions can be expressed in terms of hypergeometric functions. We…
A unified approach, for solving a wide class of single and many-body quantum problems, commonly encountered in literature is developed based on a recently proposed method for finding solutions of linear differential equations. Apart from…