Dissipative Kerr solitons in optical microresonators with Raman effect and third-order dispersion

Using the mean-field normalized Lugiato-Lefever equation,we theoretically investigate the dynamics of cavity soliton and comb generation in the presence of Raman effect and the third-order dispersion.Both of them can induce the temporal drift and frequency shift.Based on the moment analysis method,we analytically obtain the temporal and frequency shift,and the results agree with the direct numerical simulation.Finally,the compensation and enhancement of the soliton spectral between the Raman-induced self-frequency shift and soliton recoil are predicted.Our results pave the way for further understanding the soliton dynamics and spectral characteristics,and providing an effective route to manipulate frequency comb.

(2+1)-dimensional dissipation nonlinear Schrdinger equatio for envelope Rossby solitary waves and chirp effect

In the past few decades, the （1 ＋ 1）-dimensional nonlinear Schr6dinger （NLS） equation had been derived for envelope Rossby solitary waves in a line by employing the perturbation expansion method. But, with the development of theory, we note that the （1＋1）-dimensional model cannot reflect the evolution of envelope Rossby solitary waves in a plane. In this paper, by constructing a new （2＋1）-dimensional multiscale transform, we derive the （2＋1）-dimensional dissipation nonlinear Schrodinger equation （DNLS） to describe envelope Rossby solitary waves under the influence of dissipation which propagate in a plane. Especially, the previous researches about envelope Rossby solitary waves were established in the zonal area and could not be applied directly to the spherical earth, while we adopt the plane polar coordinate and overcome the problem. By theoretical analyses, the conservation laws of （2＋ 1）-dimensional envelope Rossby solitary waves as well as their variation under the influence of dissipation are studied. Finally, the one-soliton and two-soliton solutions of the （2＋ 1）-dimensional NLS equation are obtained with the Hirota method. Based on these solutions, by virtue of the chirp concept from fiber soliton communication, the chirp effect of envelope Rossby solitary waves is discussed, and the related impact factors of the chirp effect are given.

色散和耗散对Alfven孤立波的影响

利用变数变换和解析积分的方法，分别找到了带色散项的ＤＮＬＳ方程和带耗散的ＭＫｄＶ方程的一类解析解，给出了存在孤立波的条件．

水波动力学研究进展

水波动力学，历史悠久，内容丰富，此文仅进行简要的历史回顾，以阐明其进展的思想、智慧、途径以及这门学科对其它学科进展的贡献和影响．随后，引进一个新理论，能模拟三维、非定常、有完全非线性和频散（或色散）性的重力毛细波，在深度任变的水中传播和演化的现象．此外，对二维水波在海滩上之涨落问题，提供一个Ｌａｇｒａｎｇｅ－Ｅｕｌｅｒ观点相结合的精确计算方法，以供读者推广和应用，此外，对外力作用下的水波系统共振现象，作些补充论述．

基于扩展型双曲缓坡方程波浪传播模型

在时域缓坡方程中,引入非线性修正项、高阶地形影响项以及能量耗散项,推导得出扩展型双曲缓坡方程。基于该方程,利用ADI格式建立波浪传播数学模型,并应用于椭圆形浅滩、Bragg反射正弦沙涟地形以及斜坡地形的波浪传播计算,计算结果与试验数据均吻合良好,表明该模型能够对近岸波浪的折射、绕射、反射、浅水变形、弱非线性、陡变地形影响以及破碎进行较好地模拟。

基于双光束耦合的双光子全息屏蔽光伏空间孤子

证明了在双光束耦合外加偏压的双光子光伏光折变晶体中存在一种新的全息屏蔽光伏空间孤子。在信号光远小于抽运光的条件下得出了亮(暗)孤子的解析解。数值模拟了这种孤子在稳态条件下的演化特性。结果表明:在给定的参量情况下,在晶体中可形成稳定的双光子明(暗)全息屏蔽光伏空间孤子。