*Correspondence: [email protected] Department of Mathematics, Huaihua University, Huaihua, 418008, China Abstract In this paper, we consider the initial value problem for a two-dimensional generalized Zakharov system with quantum effects. We prove the existence and uniqueness of global smooth solutions to the initial value problem in the Sobolev space through making a priori integral estimates ...

We prove the local well-posedness of the three-dimensional Zakharov-Kuznetsov equation ∂tu+∆∂xu+u∂xu = 0 in the Sobolev spaces Hs(R3), s > 1, as well as in the Besov space B 2 (R 3). The proof is based on a sharp maximal function estimate in time-weighted spaces.

NUCLEAR-MEDIUM MODIFICATION OF THE ρ(1S)AND ρ(2S)-MESONS IN COHERENT PHOTOAND ELECTROPRODUCTION: COUPLED CHANNEL ANALYSIS N.N. Nikolaev, J. Speth and B.G. Zakharov Institut für Kernphysik, Forschungszentrum Jülich, D-52425 Jülich, Germany Landau Institute for Theoretical Physics, GSP-1, 117940, Kosygina Str. 2, 117334 Moscow, Russia

We apply an analogue of the Zakharov-Shabat dressing method to obtain infinite matrix solutions to the Toda lattice hierarchy. Using an operator transformation we convert some of these into solutions in terms of integral operators and Fredholm determinants. Others are converted into a class of operator solutions to the l-periodic Toda hierarchy.

We describe the direct experimental measurement of the transverse propagation velocities of dark spatial solitons. Good agreement is obtained from a comparison of the velocities measured experimentally and the velocities predicted by the two-dimensional theory of Zakharov and Shabat [Sov. Phys. JETP 37, 823 (1973)].

We derive a determinant formula for the WKB exponential of singularly perturbed Zakharov-Shabat system that corresponds to the semiclassical (zero dispersion) limit of the focusing Nonlinear Schrödinger equation. The derivation is based on the RiemannHilbert Problem (RHP) representation of the WKB exponential. We also prove its independence of the branchpoints of the corresponding hyperelliptic...

Roald Zinnurovich Sagdeev (on his 90th birthday), Aganbegyan A.G., Vainshtein A.I., Dudnikova G.I., Zakharov V.E., Zelenyi L.M., Kuznetsov E.A., Litvak Nigmatulin R.I., Ryutov D.D., Skrinskii A.N., Sunyaev R.A., Fedoruk M.P.

Based on recent studies by Guy Jumarie [1] which defines probability density of fractional order and fractional moments by using fractional calculus (fractional derivatives and fractional integration), this study expands the concept of probability density of fractional order by defining the fractional probability measure, which leads to a fractional probability theory parallel to the classical ...