On Some Canonical Classes of Cubic-Quintic Nonlinear Schrödinger Equations

具有线性自耦合和交叉耦合项的混合耦合非线性薛定谔方程中亮孤子的周期能量开关

Periodic energy switching of bright solitons in mixed coupled nonlinear Schr{ö}dinger equations with linear self and cross coupling terms

通过确定一个变换将相应的方程变换为可积的混合2-CNLS方程，得到了具有线性自耦合和交叉耦合项的混合2-耦合非线性Schr{<$}dinger（CNLS）方程的亮孤子解.对亮孤子碰撞动力学的研究表明，由于耦合项的存在，存在周期性的能量开关。这种周期性的能量开关可以通过混合2-CNLS系统中产生的亮孤子的新型形状变化碰撞来控制，其特征在于强度重新分布、振幅相关相移和相对分离距离。我们还指出，该系统表现出大的周期性强度切换，即使很小的线性自耦合强度。

Deep-water waves: On the nonlinear Schr{ö}dinger equation and its solutions

We present a brief discussion on the nonlinear Schr{ö}dinger equation for modeling the propagation of the deep-water wavetrains and a discussion on its doubly-localized breather solutions that can be connected to the sudden formation of extreme waves, also known as rogue waves or freak waves.

变系数五阶非线性薛定谔方程的对称性分类

Symmetry classification of variable coefficient cubic-quintic nonlinear Schrödinger equations

本文在等价变换的作用下，对含5个任意时空函数的变系数五次非线性薛定谔方程进行了李代数分类.结果表明，在真正的五阶非线性中，它们的对称群至多是四维的。当方程是三次型时，它只有五维（同构于伽利略相似代数gs（1）），当方程是五次型时，它只有六维（同构于薛定谔代数sch（1））。

修正的非线性薛定谔孤子的微扰理论

Perturbation theory for the modified nonlinear Schr{ö}dinger solitons

基于Riemann-Hilbert问题，建立了描述飞秒光脉冲在非线性单模光纤中传输的修正非线性薛定谔方程的微扰理论。详细分析了微扰诱导孤子参数演化的绝热近似。线性微扰和拉曼增益被认为是作为例子。

Peregrine comb: multiple compression points for Peregrine rogue waves in periodically modulated nonlinear Schr{ö}dinger equations

It is shown that sufficiently large periodic modulations in the coefficients of a nonlinear Schr{ö}dinger equation can drastically impact the spatial shape of the Peregrine soliton solutions: they can develop multiple compression points of the same amplitude, rather than only a single one, as in the spatially homogeneous focusing nonlinear Schr{ö}dinger equation. The additional compression points are generated in pairs forming a comb-like structure. The number of additional pairs depends on the amplitude of the modulation but not on its wavelength, which controls their separation distance. The…

非克尔介质中含五阶非线性项的耦合非线性薛定谔方程：可积性和孤子相互作用

Coupled nonlinear Schrodinger equations with cubic-quintic nonlinearity: Integrability and soliton interaction in non-Kerr media

提出了一个含五阶非线性项的耦合非线性薛定谔方程组的可积系统，用以描述非克尔介质中五阶非线性对超短光孤子脉冲传输的影响.给出了该可积模型的拉克斯对、守恒量和精确孤子解。利用双孤子的显式形式研究了孤子相互作用，显示出许多有趣的特性，包括非弹性（形状变化）散射。导出了另一个新的五阶非线性耦合方程组，它代表了已知的手征孤子轴承系统的矢量推广。