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We use 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 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.

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We develop a unified approach to integrating the Whitham modulation equations. Our approach is based on the formulation of the initial-value problem for the zero-dispersion KdV as the steepest descent for the scalar Riemann-Hilbert problem [6] and on the method of generating differentials for the KdV-Whitham hierarchy [9]. By assuming the hyperbolicity of the zero-dispersion limit for the KdV with general initial data, we bypass the inverse scattering transform and produce the symmetric system of algebraic equations describing motion of the modulation parameters plus the system of inequalities determining the number the oscillating phases at any fixed point on the (x, t)-plane. The resulting system effectively solves the zero-dispersion KdV with an arbitrary initial datum.

A randomized controlled study included 44 patients with acute myocardial infarction. It was found that intracoronary injection of bone marrow mononuclear cells is safe, ensures fixation of the injected cells in the myocardium, reduces blood levels of IL-1beta and TNF-alpha, increases the content insulin-like growth factor, and does not provoke malignant arrhythmias.

A soliton-type erbium-doped all-fiber ring laser hybrid mode-locked with a co-action of arc-discharge single-walled carbon nanotubes (SWCNTs) and nonlinear polarization evolution (NPE) is demonstrated. For the first time, to the best of our knowledge, boron nitride-doped SWCNTs were used as a saturable absorber for passive mode-locking initiation. Moreover, the NPE was introduced through the implementation of the short-segment polarizing fiber. Owing to the NPE action in the laser cavity, significant pulse length shortening as well as pulse stability improvement were observed as compared with a SWCNTs-only mode-locked laser. The shortest achieved pulse width of near transform-limited solitons was 222 fs at the output average power of 9.1 mW and 45.5 MHz repetition frequency, corresponding to the 0.17 nJ pulse energy.