具量子效应Zakharov方程弱解的存在性

Zakharov方程具有丰富的物理背景．通过Arzela－Ascoli定理、Faedo－Galerkin方法和紧性原理,得到等离子体模型中具量子效应Zakharov方程弱整体解的存在性．     

Zakharov格点动力系统的指数吸引子

利用一般格点动力系统存在指数吸引子的充分条件,证明自治Zakharov格点动力系统的指数吸引子的存在性.     

格点量子Zakharov方程组紧致核截面的存在性与熵的估计

讨论一类非自治带量子纠正的修正Zakharov方程组在无穷格点上解的渐近行为,应用截断函数的技巧证明该格点方程组紧致核截面的存在性,并给出核截面的Kolmogorov-ε熵的上界估计.     

Global random attractors for the stochastic dissipative Zakharov equations

The stochastic dissipative Zakharov equations with white noise are mainly investigated. The global random attractors endowed with usual topology for the stochastic dissipative Zakharov equations are obtained in the sense of usual norm. The method is to transform the stochastic equations into the corresponding partial differential equations with random coefficients by Ornstein-Uhlenbeck process. The crucial compactness of the global random attractors wiil be obtained by decomposition of solutions.     

带磁场的广义Zakharov模型的奇异解

该文研究了带磁场的广义Zakharov模型的奇异解.得到了带磁场的广义Zakharov模型奇异解存在的充分条件,以及奇异解的下界速率.     

非均匀介质中Zakharov系统的位力奇性解

研究非均匀介质中Zakharov系统的位力奇性解.该系统描述了静电势与等离子密度在静电极限意义下的相互作用.一方面,利用位力恒等式,在c₀=+∞时证明了所研究的Zakharov系统的有限时间爆破结果.另一方面,通过建立局部的位力恒等式并利用关于时间的Lyapunov函数的存在性,在00<+∞时得到了所研究的Zakharov系统具负能量的径向对称解的爆破结果.     

离子声学模型Zakharov方程组的整体吸引子的存在性(英文)

In this paper,we consider the initial-boundary problem for Zakharov equations arising from ion-acoustic modes and obtain the existence of global attractor for the initialboundary problem for Zakharov equations.     

The Jacobi Elliptic Function Method for Solving Zakharov Equation

The Zakharov equation to describe the laser plasma interaction process has very important sense, this paper gives the solitary wave solutions for Zakharov equation by using Jacobi elliptic function method.     

一类广义Zakharov方程的精确行波解

本文研究了一类广义Zakharov方程的精确解行波解的问题.利用改进的G/G展开方法,借助于计算机代数系统Mathematica,获得了具有重要物理背景的广义Zakharov方程一系列新的含有多个参数的精确行波解,这些解包括孤立波解,双曲函数解,三角函数解,以及有理函数解.     

一个推广的Zakharov系统的亚音速极限(英文)

本文研究三维空间中一个具有阻尼项的推广的Zakharov系统的亚音速极限,给出从Zakharov到非线性Schrdinger方程形式极限的严格数学证明.利用弱紧性讨论和能量方法建立了弱收敛和强收敛结果.此外,还需指出,频率分解技术和Strichartz估计对强收敛性的证明是非常有用的.     

STRANGE ATTRACTORS ON PSEUDOSPECTRAL SOLUTIONS FOR DISSIPATIVE ZAKHAROV EQUATIONS

In this paper, the pseudospectral method to solve the dissipative Zakharov equations is used. Its convergence is proved by priori estimates. The existence of the global attractors and the estimates of dimension are presented. A class of steady state solutions is also disscussed. The numerical results show that if the steady state solutions satisfy some special conditions, they become unstable and limit cycles and strange attractors will occur for very small perturbations . The largest Lyapunov exponent and analysis of the linearized system are applied to explain these phenomena.     

EXACT TRAVELING WAVE SOLUTIONS OF MODIFIED ZAKHAROV EQUATIONS FOR PLASMAS WITH A QUANTUM CORRECTION＊

In this article,the authors study the exact traveling wave solutions of modified Zakharov equations for plasmas with a quantum correction by hyperbolic tangent function expansion method,hyperbolic seca...     

Attractors and Dimensions for Discretizations of a Dissipative Zakharov Equations

Abstract In this paper, a dissipative Zakharov equations are discretized by difference method.We make priorestimates for the algebric system of equations. It is proved that for each mesh size,there exist attractors forthe discretized system.The bounds of the Hausdorff dimensions of the discrete attractors are obtained,and thevarious bounds are dependent of the mesh sizes.     

New exact travelling wave solutions of two nonlinear physical models

In this paper, an improved tanh function method is used with a computerized symbolic computation for constructing new exact travelling wave solutions on two nonlinear physical models namely, the quantum Zakharov equations and the (2+1)-dimensional Broer–Kaup–Kupershmidt (BKK) system. The main idea of this method is to take full advantage of the Riccati equation which has more new solutions.The exact solutions are obtained which include new soliton-like solutions, trigonometric function solutions and rational solutions. The method is straightforward and concise, and its applications are promising.     

On the global existence and small dissipation limit for generalized dissipative Zakharov system

This paper deals with the existence and uniqueness of the global solutions to the initial boundary value problem for a generalized Zakharov system with direct self‐interaction of the dispersive waves and weak dissipation in the nondispersive subsystem. We prove the global existence of the generalized solution to the problem by a priori estimates and Galerkin method. We also establish the regularity of the global generalized solution and the existence and uniqueness of the global classical solution. Moreover, we obtain the convergence of the solutions of the generalized Zakharov system with dissipation as the dissipative coefficient approaches zero.     

耗散力学和非线性耗散型方程的精确解——耗散力学原理和应用(Ⅰ)

本文是文[1～4]的继续和升华.(1)在本文中,我们根据互补性原理,建立了耗散力学.它是与量子力学相对应的一种耗散理论.可以用这种理论来统一地处理非平衡态热力学和粘滞流体动力学问题,并可以用它来处理量子力学中各种耗散和不可逆的问题.耗散力学的基本方程是与Schr?dinger方程或Dirac方程相对应的一类本征值方程;(2)在本文中,我们将一些基本的非线性耗散型方程,特别是作为宏观非平衡态热力学和粘滞流体动力学基本方程的Navier-Stokes方程,统一地归结为耗散力学基本方程的可积性条件,从而为利用散射反演方法求它们的精确解扫平了道路.     

Cnoidal and snoidal wave solutions to coupled nonlinear wave equations by the extended Jacobi’s elliptic function method

This paper studies two nonlinear coupled evolution equations. They are the Zakharov equation and the Davey–Stewartson equation. These equations are studied by the aid of Jacobi’s elliptic function expansion method and exact periodic solutions are extracted. In addition, the Zakharov equation with power law nonlinearity is solved by traveling wave hypothesis.