玻色-爱因斯坦凝聚体中的怪波操控

利用Darboux变换法, 解析地研究了玻色-爱因斯坦凝聚体(BEC)中的怪波. 结果表明: 当谱参数等于非线性系数时, BEC中形成一种新型的单洞怪波; 而当谱参数小于非线性系数时, BEC中出现双洞怪波. 进一步地, 怪波的出现位置可通过调节周期性势阱的驱动频率和强度来控制. 此外, 随着原子间相互作用的减小, 怪波的最高幅度也随之降低. 相关结果可为预防怪波的危害提供帮助.     

玻色-爱因斯坦凝聚体中的怪波操控

利用Darboux变换法, 解析地研究了玻色-爱因斯坦凝聚体(BEC)中的怪波. 结果表明: 当谱参数等于非线性系数时, BEC中形成一种新型的单洞怪波; 而当谱参数小于非线性系数时, BEC中出现双洞怪波. 进一步地, 怪波的出现位置可通过调节周期性势阱的驱动频率和强度来控制. 此外, 随着原子间相互作用的减小, 怪波的最高幅度也随之降低. 相关结果可为预防怪波的危害提供帮助.     

玻色-爱因斯坦凝聚体中的怪波操控

利用Darboux变换法,解析地研究了玻色-爱因斯坦凝聚体(BEC)中的怪波.结果表明:当谱参数等于非线性系数时,BEC中形成一种新型的单洞怪波;而当谱参数小于非线性系数时,BEC中出现双洞怪波.进一步地,怪波的出现位置可通过调节周期性势阱的驱动频率和强度来控制.此外,随着原子间相互作用的减小,怪波的最高幅度也随之降低.相关结果可为预防怪波的危害提供帮助.     

空间位移PT对称非局域非线性薛定谔方程的高阶怪波解

利用Kadomtsev-Petviashvili(KP)系列约束方法和双线性方法,构造了空间位移宇称-时间反演(PT)对称非局域非线性薛定谔方程的高阶怪波解.任意N阶怪波解的解析表达式是通过舒尔多项式表示的.首先通过分析一阶怪波解的动力学行为,发现怪波的最大振幅可以大于背景平面三倍的任意高度.分析了对称非局域非线性薛定谔方程中的空间位移因子x₀在一阶怪波解中的影响,结果表明其仅改变怪波中心的位置.另外,研究了二阶怪波解的动力学行为以及怪波模式,然后给出了N阶怪波模式与N阶怪波解的解析表达式中参数之间的关系,进一步展示了高阶怪波的不同模式.     

大尺度浅水波方程中相互调制的非线性波

基于一般的浅水波方程, 根据大尺度正压大气的特点, 得到无量纲的控制大尺度大气的动力学非线性方程组. 利用多尺度法, 由无量纲的动力学方程组导出了扰动位势的非线性控制方程. 采用椭圆方程构造该扰动位势控制方程的解, 获得了扰动位势和速度的多周期波与冲击波(爆炸波) 并存的解析解. 扰动位势的解表明经向和纬向具有不同周期和波长的周期波, 且都受纬向孤波的调制; 速度的解表明大尺度大气流动存在气旋和反气旋周期性分布的现象. 关键词： 浅水波方程 大尺度正压大气 解析解 非线性波     

非线性振动、非线性波与Jacobi椭圆函数

介绍用较易懂且简捷的Jacobi椭圆函数解法求非线性振动与非线性波的解析解,并以单摆,达芬(Duffing)振子,KdV方程,正弦戈登(Gordon)方程(SG方程),非线性薛定谔方程(NLS方程)的椭圆函数解,钟形孤立波解,扭结与反扭结波解,呼吸子解,扭结波与反扭结波迎头碰撞及包络型孤立子波解等重要实例,给出了说明．     

弹性管中的怪波

利用约化摄动法,推导了流体在弹性管中的非线性薛定谔方程(NLSE).由非线性薛定谔方程的解来近似地描述出真实的怪波,继而研究怪波解中各个参数对怪波系统振幅、波速的影响.最后将这一模型应用到人体血管中,研究怪波在人体动脉血管中传播对人体健康的影响.     

非线性薛定谔方程的孤波解

通过行波变换把非线性薛定谔方程化为常微分方程,并利用黎卡提投影方程映射法得到了非线性薛定谔方程的孤波解.     

从立方抛物线谈起(2)--余弦型行波,椭圆余弦型行波与孤立波

从立方抛物线的特性谈起，用较初浅的方法，借助于雅可比椭圆函数求椭圆方程的解，说明一类非线性波方程可用行波法求解析解．求得了许多非线性波的重要性质，特别是求得孤立波解．举KdV方程、正弦-Gordon方程(SG方程)、非线性薛定谔方程(NLS)及mKdV方程为典型实例．     

阻尼作用下一维非线性单原子链中的孤子

利用多重尺度法,研究了弱阻尼作用下一维非线性单原子链中的波动行为,发现在O(ε)级阻尼作用下其格波幅度减小,群速变慢.在晶格动力学中导出了参数耗散型非线性Schrdinger方程,对方程进行解析求解.结果表明在O(ε)级阻尼作用下一维非线性单原子链中的格孤波为传播的包络孤子;在O(ε2)级阻尼作用下,格孤波为钟状或扭结的孤子.     

Rogue wave solutions for the coupled cubic–quintic nonlinear Schrödinger equations in nonlinear optics

A generalized Darboux transformation for the coupled cubic–quintic nonlinear Schrödinger equation is constructed by the Darboux matrix method. As applications, the Nth-order rogue wave solutions of the coupled cubic–quintic nonlinear Schrödinger equation have been obtained. In particular, the dynamics of the general first- and second-order rogue waves are discussed and illustrated through some figures.     

光纤放大器中非自治光畸波的传播控制研究

本文采用一个通用的理论,即用相似变换的方法,研究构建了(1+1)维变系数非线性薛定谔方程的精确畸形波解,首先讨论了一阶光畸波在光纤放大器中的传播问题.发现光学畸波的特性,如宽度、振幅和位置,可通过非线性光学介质特性和光脉冲的初始参量进行控制;然后在选择可控参数条件下,讨论了可控光畸波在非线性介质的传播行为,包括延迟激发、抑制、以及保持.这在理论和实际应用上具有启迪价值.     

On Nth-order rogue wave solution to the generalized nonlinear Schrödinger equation

In this Letter, the generalized nonlinear Schrödinger (GNLS) equation is investigated by Darboux matrix method. A generalized Darboux transformation (DT) of the GNLS equation is constructed with the help of the gauge transformation for an Ablowitz–Kaup–Newell–Segur (AKNS) type GNLS spectral problem, from which a unified formula of Nth-order rogue wave solution to the GNLS equation is given. In particular, the first and second-order rogue wave solutions to the GNLS equation are explicitly illustrated through some figures.     

Analytical solutions and rogue waves in (3+1)-dimensional nonlinear Schrödinger equation

Analytical solutions in terms of rational-like functions are presented for a (3+1)-dimensional nonlinear Schrödinger equation with time-varying coefficients and a harmonica potential using the similarity transformation and a direct ansatz. Several free functions of time t are involved to generate abundant wave structures. Three types of elementary functions are chosen to exhibit the corresponding nonlinear rogue wave propagations.     

Localized waves in three-component coupled nonlinear Schrdinger equation

We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,we get the interactional solutions between first-order rogue wave and one-dark,one-bright soliton respectively.Meanwhile,the interactional solutions between one-breather and first-order rogue wave are also given.In second-order localized wave,one-dark-one-bright soliton together with second-order rogue wave is presented in the first component,and two-bright soliton together with second-order rogue wave are gained respectively in the other two components.Besides,we observe second-order rogue wave together with one-breather in three components.Moreover,by increasing the absolute values of two free parameters,the nonlinear waves merge with each other distinctly.These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system.     

Solitary waves and rogue waves in a plasma with nonthermal electrons featuring Tsallis distribution

In this Letter, we discuss the electron acoustic (EA) waves in plasmas, which consist of nonthermal hot electrons featuring the Tsallis distribution, and obtain the corresponding governing equation, that is, a nonlinear Schrödinger (NLS) equation. By means of Modulation Instability (MI) analysis of the EA waves, it is found that both electron acoustic solitary wave and rogue wave can exist in such plasmas. Basing on the Darboux transformation method, we derive the analytical expressions of nonlinear solutions of NLS equations, such as single/double solitary wave solutions and single/double rogue wave solutions. The existential regions and amplitude of solitary wave solutions and the rogue wave solutions are influenced by the nonextensive parameter q and nonthermal parameter α. Moreover, the interaction of solitary wave and how to postpone the excitation of rogue wave are also studied.     

On the characterization of vector rogue waves in two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients

We construct vector rogue wave solutions of the two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients, namely diffraction, nonlinearity and gain parameters through similarity transformation technique. We transform the two-dimensional two coupled variable coefficients nonlinear Schrödinger equations into Manakov equation with a constraint that connects diffraction and gain parameters with nonlinearity parameter. We investigate the characteristics of the constructed vector rogue wave solutions with four different forms of diffraction parameters. We report some interesting patterns that occur in the rogue wave structures. Further, we construct vector dark rogue wave solutions of the two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients and report some novel characteristics that we observe in the vector dark rogue wave solutions.