Consideration in this present paper is the long-time asymptotics of solutions to derivative nonlinear Schrödinger (DNLS) equation with step-like initial value q(x,0)=q0(x)=A1eiϕe2iBx,x<0,A2e−2iBx,x>0,by Deift-Zhou method. The problem described by a matrix Riemann-Hilbert problem. A crucial ingredient used introduce g-function mechanism for solving entries jump growing exponentially as t→∞. It s...

Additive tree functionals represent the cost of many divide-andconquer algorithms. We derive the limiting distribution of the additive functionals induced by toll functions of the form (a) nα when α > 0 and (b) log n (the so-called shape functional) on uniformly distributed binary search trees, sometimes called Catalan trees. The Gaussian law obtained in the latter case complements the central ...

Sliding-frequency filter systems are known to admit two families of accelerating solitons: high-amplitude and low-amplitude families. Such equilibrium solutions are computed here, for a wide range of filter strengths, as self-similar solutions having Airy function asymptotics. In a limited parameter region, the profile possesses a secondary small hump. The high-amplitude solitons are found to b...

We present a numerical study of the giant Goos-Hänchen shifts (GHSs) obtained from an Airy beam impinging on a nonlinear interface. To avoid any angular restriction associated with the paraxial approximation, the analysis is based on the nonlinear Helmholtz equation. We report the existence of nonstandard nonlinear GHSs displaying an extreme sensitivity to the input intensity and the existence ...

We derive integral formulas, involving the Airy function, for moments of the time a two-sided Brownian motion with parabolic drift attains its maximum.