Related papers: Solution to the evolution equation at NLL for high…
We give the solution to the complete noncommutative Kadomtsev--Petviashvili (KP) hierarchy. We achieve this via direct linearisation which involves the Gelfand--Levitan--Marchenko (GLM) equation. This is a linear integral equation in which…
Convergence of a full discretization of a second order stochastic evolution equation with nonlinear damping is shown and thus existence of a solution is established. The discretization scheme combines an implicit time stepping scheme with…
By the Sylvester equation $\bL\bM-\bM\bK=\br\bs^{\st}$ together with an evolution equation set of $\br$ and $\bs$, generalized Cauchy matrix approach is established to investigate exact solutions for Kadomtsev-Petviashvili system, including…
Cubic regularization (CR) is an optimization method with emerging popularity due to its capability to escape saddle points and converge to second-order stationary solutions for nonconvex optimization. However, CR encounters a high sample…
In this paper, we consider the long time behavior of solution to the quadratic gauge invariant nonlinear Klein-Gordon equation (NLKG) in two space dimensions. For a given asymptotic profile, we construct a solution to (NLKG) which converges…
We compute the Next-to-Next-to-Leading Order (NNLO) QCD corrections to the partonic reaction that dominates top-pair production at the Tevatron. This is the first ever NNLO calculation of an observable with more than two colored partons,…
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…
One of the most challenging open problems in heavy quarkonium physics is the double charm production in $e^+e^-$ annihilation at B factories. The measured cross section of $e^+ e^- \to J/\psi + \eta_c$ is much larger than leading order (LO)…
We consider the damped nonlinear Schr\''{o}dinger equation with saturation: i.e., the complex evolution equation contains in its left hand side, besides the potential term $V(x)u,$ a nonlinear term of the form $\mathrm{i}\mu…
Approximating periodic solutions to the coupled Duffing equations amounts to solving a system of polynomial equations. The number of complex solutions measures the algebraic complexity of this approximation problem. Using the theory of…
We study the Stephanov model, which is an RMT model for QCD at finite density, using the Complex Langevin algorithm. Naive implementation of the algorithm shows convergence towards the phase quenched or quenched theory rather than to…
Exploiting recently obtained analytic solutions of classical Yang-Mills equations for higher order perturbations in the field of the dilute object (proton), we derive the complete first saturation correction to the single inclusive…
We provide a complete and detailed study of the high-energy limit of four-parton scattering amplitudes in QCD, giving explicit results at two loops and higher orders, and going beyond next-to-leading logarithmic (NLL) accuracy. Building…
Hierarchical decays of $N$ matter species to radiation may balance against Hubble expansion to yield stasis, a new phase of cosmological evolution with constant matter and radiation abundances. We analyze stasis with various machine…
The strong coupling $\alpha_s$ is determined with high precision from fits to lattice QCD simulations on the static energy. Our theoretical setup relies on R-improving the three-loop fixed-order prediction for the static energy by removing…
In this paper, we study large time behavior of complex-valued solutions to nonlinear Klein-Gordon equation with a gauge invariant quadratic nonlinearity in two spatial dimensions. To find a possible asymptotic behavior, we consider the…
``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…
We cure the perturbative instability of the total-inclusive-photoproduction cross sections of vector $S$-wave quarkonia observed at high photon-proton-collision energies ($\sqrt{s_{\gamma p}}$) in Next-to-Leading Order (NLO)…
We consider the Lagrange density of non-relativistic Quantum Chromodynamics expanded up to order $1/m^2$, where $m$ is the heavy quark mass, and compute several matching coefficients up to two-loop order. Our results are building blocks for…
The decay $B \to X_s \gamma$ is studied at the Next to Leading Order in QCD in a class of models containing at least two Higgs doublets and with only one charged Higgs boson non-decoupled at low-energy. The two-loop matching condition is…