Alexander Krylov

Decay of an initial discontinuity in the defocusing NLS hydrodynamics

Abstract A complete classification s presented for the problem of an initial discontinuity in the NLS hydrodynamics. Appearance and properties of so-called “vacuum point” inside the nondissipative shock wave are studied.

Modulational instability and formation of a nonlinear oscillatory structure in a focusing' medium

Abstract The self-similar decay of the uniform envelope of an unstable wave described by the “focusing” nonlinear Schrodinger equation is studied. The exact analytic solution of the appropriate elliptic Whitham averaged system is obtained.

General solution of the Cauchy problem for the defocusing NLS equation in the Whitham limit

A general solution is obtained for the Whitham-NLS system with Gurevich-Pitaevskii-like matching conditions.

Soliton turbulence as a thermodynamic limit of stochastic soliton lattices

Abstract We use the recently introduced notion of stochastic soliton lattice for quantitative description of soliton turbulence. We consider the stochastic soliton lattice on a special band-gap scaling of the spectral surface of genus N so that the integrated density of states remains finite as N→∞ (thermodynamic type limit). We prove existence of the limiting stationary ergodic process and associate it with the homogeneous soliton turbulence. The phase space of the soliton turbulence is a one-dimensional space with the random Poisson measure. The zero-density limit of the soliton turbulence coincides with the Frish–Lloyd potential of the quantum theory of disordered systems.

GRADIENT-CONSISTENT NON-LINEAR MODEL OF THE GENERATION OF ULTRASOUND IN THE PROPAGATION OF SEISMIC WAVES?

Abstract The equations of the propagation of weak non-linear waves are obtained by a detailed analysis of the gradient-consistent micropolar model of a granular continuous medium. The high-frequency mode of oscillation is associated with ultrasonic waves, and the low-frequency mode is associated with the usual seismic waves in rocks. The evolution equations that include the case of long-wave-short-wave resonance are obtained by an asymptotic consideration. This resonance corresponds to the case of the generation of ultrasound (noise) by travelling seismic waves.

Nondissipative shock waves in two-phase flows

It is shown that the Korteweg-de Vries equation which describes dissipationless processes can occur also in the system of equations of multiphase hydrodynamics when dissipation is compensated by external supply of energy. Therefore all the phenomena which are characteristic for the Korteweg-de Vries equation (solitons, periodic waves, nondissipative shock waves) can occur also in multiphase hydrodynamics. The study analyzes in particular the phenomenon of formation of nondissipative shock waves. It is shown that multiphase filtration is accompanied by formation of a continuously expanding region with small scale undamping oscillations of phase composition and velocity. The analysis uses the Korteweg-de Vries equation which is derived from the system of conservation laws describing multiphase hydrodynamics in porous media. Obtained results are relevant for the analysis of multiphase filtration (viscous fingering in the hydrocarbon recovery process) and in the hydrodynamics of fluidized bed (formation of bubbles).

Stable Similariton Generation in an All-Fiber Hybrid Mode-Locked Ring Laser for Frequency Metrology

Ultrashort pulse lasers constitute an important tool in the emerging field of optical frequency metrology and are enabling unprecedented measurement capabilities and new applications in a wide range of fields, including precision spectroscopy, atomic clocks, ultracold gases, and molecular fingerprinting. We demonstrate the generation of stable 127-fs self-similar pulses at a central wavelength of 1560 nm with 7.14-mW average output power. Similariton lasers have a low repetition rate deviation in the averaging time interval 1-1·103 s, a low relative intensity noise -120 dBc/Hz (30 Hz to 10 kHz), a narrow single comb line width of 32 kHz, and high reliability. Thus, such lasers are highly promising for further development of the stabilized combs and open up a robust and substantially simplified route to synthesizing low-noise microwaves.

Breaking Problem in Dispersive Hydrodynamics

Whitham modulation equations1 are investigated very actively last time. This is caused by theoretical aspects of general theory of hydrodynamic type systems2, as well as by the importance of physical applications, most interesting of which are nondissipative shock waves (NSW). It is well known that wave breaking of the simple Riemann wave3 in dispersive hydrodynamics leads to the appearance of continuously expanding region filled with undamped small-scale nonlinear oscillations. This is NSW. First the shock wave problem in dispersive hydrodynamics - Gurevich-Pitaevsky (GP) problem - was considered in Ref. 4, where analytic solution of the problem of an initial discontinuity decay in KdV hydrodynamics was obtained and numerical analysis of the simple wave breaking was done. Then this topic was developed in Refs. 5–10. The important property of modulation sets for KdV, NLS and SG-equations which was effectively used in these works is the possibility to represent them in characteristic (Riemann) form.11–13 partially this fact allowed to introduce important concept of quasi-simple wave and receive some exact NSW-solutions.8,9

Comb characterization of Erbium All-fiber Hybrid Mode-locked ultra-short pulse Ring laser for Frequency Metrology

Stable 92.6 fs dechirped self-similar pulses were obtained at 1560 nm with 11.2 mW average output power. Similariton laser has low repetition rate deviation at 1 - 103 s, a single comb linewidth of 110 kHz and high reliability, which makes it promising for further development of the stabilized comb.

Dissipative soliton resonance in Bismuth-doped fiber laser

We experimentally demonstrate the generation of dissipative soliton resonance (DSR) in a passively mode-locked Bi-doped fiber ring laser based on nonlinear polarization rotation (NPR) technique. The DSR with the central wavelength of 1169.5 nm has a repetition rate of 343.7 kHz. By purely increasing the pump power, the DSR evolves from Gaussian shape to rectangular shape with the duration extending from 2.1 ns to 13.1 ns, while keeping the pulse amplitude and the 3-dB spectrum bandwidth almost constant. The single-pulse energy reaches 24.82 nJ. Furthermore, we construct a lumped model to reproduce the mode-locking process and the traits of the DSR pulse. The obtained results indicate that it could achieve higher pulse energy in mode-locked Bi-doped fiber laser by generating DSR.