We study the scattering theory for the Zakharov equation in three space dimensions. We show the unique existence of the solution for this equation which tends to the given free profile with no restriction on the size of the scattered states and on the support of the Fourier transform of them. This yields the existence of the pseudo wave operators.

In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...

In this paper, the convergence of Zakharov-Kuznetsov (ZK) equation by homotopy analysis method (HAM) is investigated. A theorem is proved to guarantee the convergence of HAM and to find the series solution of this equation via a reliable algorithm. c ⃝ 2014 IAUCTB. All rights reserved.

The inverse scattering problem for coupled wave equations has various applications such as waveguide filter design and electric transmission line fault diagnosis. In this paper, an efficient numerical algorithm is presented for solving the inverse scattering problem related to generalized Zakharov-Shabat equations with two potential functions. Inspired by the work of Xiao and Yashiro on Zakharo...

In this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modified Riemann-Liouville derivative. With the aid of symbolic computation, we choose the space-time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation in mathematical physics with a source to illustrate the validity a...

Abstract

In this paper we investigate the existence of soliton solutions for a modified form of the Zakharov equations describing modulational instabilities in quantum plasmas. In particular, we show that quantum effects suppress the easily identifiable soliton solutions, obtained in the adiabatic limit. In this limit, the quantum Zakharov equations become a coupled fourth order system, not amenable to ...

The reductions of the integrable N-wave type equations solvable by the inverse scattering method with the generalized Zakharov-Shabat systems L and related to some simple Lie algebra g are analyzed. The Zakharov-Shabat dressing method is extended to the case when g is an orthogonal algebra. Several types of one soliton solutions of the corresponding N-wave equations and their reductions are stu...