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...

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...

This paper is concerned with the system of Zakharov equations which involves the interactions between Langmuir and ion-acoustic waves in plasma. Abundant explicit and exact solutions of the system of Zakharov equations are derived uniformly by using the first integral method. These exact solutions are include that of the solitary wave solutions of bell-type for n and E, the solitary wave soluti...

In this article we develop the direct and inverse scattering theory of a discrete matrix Zakharov-Shabat system with solutions Un and W n. Contrary to the discretization scheme enacted by Ablowitz and Ladik, a central difference scheme is applied to the positional derivative term in the matrix Zakharov-Shabat system to arrive at a different discrete linear system. The major effect of the new di...