N-soliton solution of a coupled integrable dispersionless equation

<正>A new coupled integrable dispersionless equation is presented by considering a spectral problem.A Darboux transformation for the resulting coupled integrable dispersionless equation is constructed with the help of spectral problems.As an application,the N-soliton solution of the coupled integrable dispersionless equation is explicitly given.     

Boiti-Leon-Pempinelli系统的新变量分离解及其方形孤子和分形孤子

利用拓展的Riccati方程映射法，得到了(2+1)维Boiti-Leon-Pempinelli系统新的变量分离 解．根据得到的分离变量解，构造出该系统新型的孤子结构——方孤子和分形孤子． 关键词： Boiti-Leon-Pempinelli系统 拓展Riccati映射 方形孤子 分形孤子     

均匀聚焦磁场中束晕-混沌的孤子控制

采用粒子.束核模型,对均匀聚焦磁场中满足K-V分布的离子束进行模拟研究.观察到束晕.混沌现象,基于束晕.混沌的非线性控制策略,提出控制束晕.混沌的孤子函数控制器,并给出具体的实施方案.模拟研究表明,运用这种方法可以消除束晕及其再生现象,达到对束晕.混沌的有效控制.     

The D'Alembert type waves and the soliton molecules in a (2+1)-dimensional Kadomtsev-Petviashvili with its hierarchy equation

For a one (2+1)-dimensional combined Kadomtsev-Petviashvili with its hierarchy equation, the missing D'Alembert type solution is derived first through the traveling wave transformation which contains several special kink molecule structures. Further, after introducing the Bäcklund transformation and an auxiliary variable, the N-soliton solution which contains some soliton molecules for this equation, is presented through its Hirota bilinear form. The concrete molecules including line solitons, breathers and a lump as well as several interactions of their hybrid are shown with the aid of special conditions and parameters. All these dynamical features are demonstrated through the different figures.     

Soliton solution and interaction property for a coupled modified Korteweg-de Vries （mKdV） system

Hirota＇s bilinear direct method is applied to constructing soliton solutions to a special coupled modified Korteweg- de Vries （mKdV） system. Some physical properties such as the spatiotemporal evolution, waveform structure, interactive phenomena of solitons are discussed, especially in the two-soliton case. It is found that different interactive behaviours of solitary waves take place under different parameter conditions of overtaking collision in this system. It is verified that the elastic interaction phenomena exist in this （1＋1）-dimensional integrable coupled model.     

Novel loop-like solitons for generalized Vakhnenko equation

A nontraveling wave solution of a generalized Vakhnenko equation arising from the high-frequent wave motion in a relaxing medium is derived via the extended Riccati mapping method. The solution includes an arbitrary function of an independent variable. Based on the solution, two hyperbolic functions are chosen to construct new solitons. Novel single-loop-like and double-loop-like solitons are found for the equation.     

MKdV方程的拟小波解

用拟小波方法求MKdV方程的数值解-先用拟小波离散格式离散空间导数，然后用四阶Runge-Kutta方法离散时间导数,对一个有精确解的实例ut+6u2ux+uxxx=0进行了数值计算-拟小波解与解析解完全重合，t=10000s时，二者也没有偏差- 关键词： MKdV方程 拟小波方法 孤子解     

非线性波方程求解的新方法

从Legendre椭圆积分和Jacobi椭圆函数的定义出发，得到了新的变换，并把它用于非线性演化方程的求解.用三个具体的例子，如非线性Klein-Gordon方程、Boussinesq方程和耦合的mKdV方程组，说明了具体的求解步骤.比较方便地得到非线性演化方程或方程组的新解析解，如周期解、孤子解等. 关键词： Jacobi椭圆函数 非线性方程 周期解 孤子解     

低阈值飞秒钛宝石激光器的理论研究

利用数值求解的方法，从理论上系统分析了决定钛宝石激光器锁模阈值的几个关键因素. 定 量分析了腔模对克尔效应的主导作用，并将光孤子模型引入低阈值锁模理论，分析了色散与 阈值的关系. 根据理论指导在实验上完成了一台阈值低至390 mW自启动飞秒掺钛蓝宝石激光 器. 关键词： 低阈值 掺钛蓝宝石激光器 克尔透镜锁模 光孤子     

Low-amplitude Screening-photovoltaic Spatial Solitons in Biased Photovoltaic Photorefractive Crystals

The low-amplitude spatial solitons in biased photovoltaic photorefractive crystals are investigated theoretically. The analytical solutions for both the bright and the dark low-amplitude screening-photovoltaic spatial solitons in photorefractive crystals are obtained. The expressions for the width of these solitons are given. The explicit expressions for the spatial deflection and angular deviation of the bright low-amplitude screening-photovoltaic spatial soliton are also presented by taking into account the effect of diffusion.