This paper continues the study, initiated in [28, 8], of the validity of the Zakharov model describing Langmuir turbulence. We give an existence theorem for a class of singular quasilinear equations. This theorem is valid for well-prepared initial data. We apply this result to the Euler-Maxwell equations describing laser-plasma interactions, to obtain, in a high-frequency limit, an asymptotic e...

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

Zakharov-Shabat–Ablowitz-Kaup-Newel-Segur (ZS–AKNS) representation for Stokes-anti-Stokes stimulated Raman scattering (SRS) is proposed. Periodical waves, solitons and self-similarity solutions are derived. Transient and bright threshold solitons are discussed. December 29, 1994 Sofia

We analytically study the long time and large space asymptotics of a new broad class solutions KdV equation introduced by Dyachenko, Zakharov, Zakharov. These are characterized Riemann--Hilbert problem which we show arises as limit $N\to \infty$ gas $N$-solitons. that this solitons in $N \to is slowly approaching cnoidal wave solution for $x - (up to terms order $\mathcal{O} (1/x)$), while zero...

We study the corresponding scattering problem for Zakharov and Shabat compatible differential equations in two-dimensions, the representation for a solution of the nonlinear Schrödinger equation is formulated as a variational problem in two-dimensions. We extend the derivation to the variational principle for the Zakharov and Shabat equations in one-dimension. We also developed an approximate a...

We are interested in the long time asymptotic behaviour of solutions to scalar Zakharov system $$\begin{aligned} \begin{array}{ll} i u_{t} + \Delta u = nu,\\ n_{tt} - n= |u|^2 \end{array} \end{aligned}$$ and Klein–Gordon–Zakharov u_{tt} one dimension space. For these two systems, we give results proving decay for initial data energy The first result deals with over compact intervals assuming sm...

the complex-step derivative approximation is applied to compute numerical derivatives. in this study, we propose a new formula of fractional complex-step method utilizing jumarie definition. based on this method, we illustrated an approximate analytic solution for the fractional cauchy-euler equations. application in image denoising is imposed by introducing a new fractional mask depending on s...

RPIC is a reduced-description particle-in-cell code designed to investigate laser-plasma instabilities in physical systems with vastly-different time scales prevalent under Inertial Confinement Fusion (ICF) conditions [1]. Such time scales include the laser, Langmuir, and ion acoustic time scales. In past literature, laser-plasma instability phenomena involving these disparate scales have mostl...

In this paper we consider the Zakharov system with periodic boundary conditions in dimension one. In the first part of the paper, it is shown that for fixed initial data in a Sobolev space, the difference of the nonlinear and the linear evolution is in a smoother space for all times the solution exists. The smoothing index depends on a parameter distinguishing the resonant and nonresonant cases...