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...

In this paper, we study the existence and uniqueness of the global smooth solution for the initial value problem of generalized Zakharov equations in dimension two. By means of a priori integral estimates and Galerkin method, we first construct the existence of global solution with some conditions. Furthermore, we prove that the global solution is unique. c ©2017 All rights reserved.

We propose a new mechanism for turbulent transport in systems which support radiating nonlinear solitary wave packets or pulses. The direct energy cascade is provided by adiabatically evolving pulses, whose widths and carrier wavelengths decrease. The inverse cascade is due to the excitation of radiation. The spectrum is steeper than the Kolmogorov-Zakharov spectrum of wave turbulence.

The inverse scattering problem method application to construction of exact solution for Maxwell dilaton gravity system ia considered. By use of Belinsky and Zakharov L A pair the solution of the theory is constructed. The rotating Kerr like configuration with NUT parameter is obtained.

In the last two decades the Inverse Spectral Transform (IST) method has been generalized and successfully applied to various (2 + 1)-dimensional nonlinear evolution equations such as Kadomtsev–Petviashvili, Davey–Stewardson, Nizhnik–Veselov–Novikov, Zakharov–Manakov system, Ishimory, two dimensional integrable sine-Gordon and others (see books [1, 2, 3, 4] and references therein). The nonlocal ...

The Zakharov equations are one of the important mathematical models in plasma physics. The solitary wave ansatz method is applied to obtain the exact solution. We use a finite difference scheme which is fourth order in space and second order in time to get a numerical solution. We show that the scheme is unconditionally stable. Numerical tests for single and interaction of two solitary waves ar...