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rogue wave solutions of (3+1)-dimensional Kadomtsev-Petviashvili equation by a direct limit method

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Communications in Theoretical Physics 2023年第6期75卷 11-21页

作者： Yujie Sun Jiaojiao Wu Biao Li School of Mathematics and Statistics Ningbo UniversityNingbo 315211China

On the bases of N-soliton solutions of Hirota’s bilinear method,high-order rogue wave solutions can be derived by a direct limit *** this paper,a(3+1)-dimensional Kadomtsev-Petviashvili equation is taken to illustrate the process of obtaining rogue waves,that is,based on the long-wave limit method,rogue wave solutions are generated by reconstructing the phase parameters of *** the fundamental pattern of rogue waves,the triangle or pentagon patterns are also ***,the different patterns of these solutions are determined by newly introduced *** the end,the general form of N-order rogue wave solutions are proposed.

关键词： rogue wave soliton Hirota bilinear method KP equation

Space Periodic Solutions and rogue wave Solution of the Derivative Nonlinear Schrodinger Equation

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Wuhan University Journal of Natural Sciences 2017年第5期22卷 373-379页

作者： ZHOU Guoquan LI Xujun School of Physics and Technology Wuhan UniversityWuhan430072HubeiChina

The derivative nonlinear Schrodinger equation, which is extensively applied in plasma physics and nonlinear optics, is analytically studied by Hirota method. Space periodic solutions are determined by means of Hirota＇s bilinear formalism, and the rogue wave solution is derived as a long-wave limit of the space periodic solution.

关键词： bilinear method the derivative nonlinear Schr?d-inger(DNLS) equation space periodic solution rogue wave

rogue waves of a(3+1)-dimensional BKP equation

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Chinese Physics B 2022年第12期31卷 21-26页

作者：袁玉强武晓昱杜仲 Department of Mathematics China University of Mining and Technology(Beijing)Beijing 100083China School of Science Beijing Forestry UniversityBeijing 100083China Department of Mathematics and Physics North China Electric Power UniversityBaoding 071003China

We investigate certain rogue waves of a(3+1)-dimensional BKP equation via the Kadomtsev-Petviashili hierarchy reduction *** obtain semi-rational solutions in the determinant form,which contain two special interactions:(i)one lump develops from a kink soliton and then fuses into the other kink one;(ii)a line rogue wave arises from the segment between two kink solitons and then disappears *** find that such a lump or line rogue wave only survives in a short time and localizes in both space and time,which performs like a rogue ***,the higher-order semi-rational solutions describing the interaction between two lumps(one line rogue wave)and three kink solitons are presented.

关键词： (3+1)-dimensional BKP equation Kadomtsev-Petviashvili hierarchy reduction interaction rogue wave lump

Symmetry and asymmetry rogue waves in two-component coupled nonlinear Schrdinger equations

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Chinese Physics B 2018年第4期27卷 236-241页

作者：李再东霍丛哲李秋艳贺鹏斌徐天赋 Department of Applied Physics Hebei University of Technology Key Laboratory of Electronic Materials and Devices of Tianjin School of Electronics and Information EngineeringHebei University of Technology School of Physics and Electronics Hunan University Hebei Key Laboratory of Microstructural Material Physics School of ScienceYanshan University

By means of the modified Darboux transformation we obtain some types of rogue waves in two-coupled nonlinear Schrodinger *** results show that the two components admits the symmetry and asymmetry rogue wave solutions,which arises from the joint action of self-phase,cross-phase modulation,and coherent coupling *** also obtain the analytical transformation from the initial seed solution to unique rogue waves with the bountiful pair *** a special case,the asymmetry rogue wave can own the spatial and temporal symmetry gradually,which is controlled by one *** is worth pointing out that the rogue wave of two components can share the temporal inversion symmetry.

关键词： rogue wave temporal inversion symmetry

Dynamics of optical rogue waves in inhomogeneous nonlinear waveguides

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Chinese Physics B 2013年第5期22卷 330-334页

作者：张解放金美贞何纪达楼吉辉戴朝卿 Zhejiang University of Media and Communications Institute of Nonlinear Physics Zhejiang Normal University School of Sciences Zhejiang Agriculture and Forestry University

We propose a unified theory to construct exact rogue wave solutions of the （2＋1）-dimensional nonlinear Schr6dinger equation with varying coefficients. And then the dynamics of the first- and the second-order optical rogues are investigated. Finally, the controllability of the optical rogue propagating in inhomogeneous nonlinear waveguides is discussed. By properly choosing the distributed coefficients, we demonstrate analytically that rogue waves can be restrained or even be annihilated, or emerge periodically and sustain forever. We also figure out the center-of-mass motion of the rogue waves.

关键词： rogue wave (2+ 1)-dimensional nonlinear Schrodinger equation inhomogeneous nonlinear waveg-uides

New Patterns of the Two-Dimensional rogue waves:(2+1)-Dimensional Maccari System

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Communications in Theoretical Physics 2017年第6期67卷 601-610页

作者：王改华王立洪饶继光贺劲松 Department of Mathematics Ningbo University School of Mechanical Engineering & Mechanics Ningbo University School of Mathematical Sciences University of Science and Technology of China

The ocean rogue wave is one kind of puzzled destructive phenomenon that has not been understood thoroughly so far. The two-dimensional nature of this wave has inspired the vast endeavors on the recognizing new patterns of the rogue waves based on the dynamical equations with two-spatial variables and one-temporal variable,which is a very crucial step to prevent this disaster event at the earliest stage. Along this issue, we present twelve new patterns of the two-dimensional rogue waves, which are reduced from a rational and explicit formula of the solutions for a(2+1)-dimensional Maccari system. The extreme points(lines) of the first-order lumps(rogue waves) are discussed according to their analytical formulas. For the lower-order rogue waves, we show clearly in formula that parameter b_2 plays a significant role to control these patterns.

关键词： (2+1)-dimensional Maccari system bilinear method rogue wave

Recent progress on optical rogue waves in fiber lasers:status,challenges,and perspectives

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Advanced Photonics 2020年第2期2卷 3-17页

作者： Yufeng Song Zhenhong Wang Cong Wang Krassimir Panajotov Han Zhang Shenzhen University Institute of Microscale OptoelectronicsCollaborative Innovation Center for Optoelectronic Science and TechnologyShenzhen Engineering Laboratory of Phosphorene and OptoelectronicsShenzhenChina Vrije Universiteit Brussel Department of Applied Physics and PhotonicsBrussels PhotonicsBrusselsBelgium Bulgarian Academy of Sciences Institute of Solid State PhysicsSofiaBulgaria

rogue waves(RWs)are rare,extreme amplitude,localized wave packets,which have received much interest recently in different areas of *** lasers with their abundant nonlinear dynamics provide an ideal platform to observe optical RW *** review recent research progress on rogue waves in fiber *** concepts of RWs and the mechanisms of RW generation in fiber lasers are discussed,along with representative experimental and theoretical *** measurement methods for RW identification in fiber lasers are presented and ***,prospects for future RW research in fiber lasers are summarized.

关键词： fiber lasers nonlinear fiber optics rogue wave

Experimental Study on the wavelengths of Two-Dimensional and Three-Dimensional Freak waves

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China Ocean Engineering 2023年第1期37卷 154-164页

作者： CUI Cheng PAN Wen-bo National Engineering Research Center for Port Hydraulic Construction Technology M.O.T.Tianjin Research Institute of Water Transport EngineeringTianjin 300456China

Freak waves are commonly characterized by strong-nonlinearity, and the wave steepness, which is calculated from the wavelength, is a measure of the degree of the wave nonlinearity. Moreover, the wavelength can describe the locally spatial characteristics of freak waves. Generally, the wavelengths of freak waves are estimated from the dispersion relations of Stokes waves. This paper concerns whether this approach enables a consistent estimate of the wavelength of freak waves. The two-(unidirectional, long-crested) and three-dimensional(multidirectional, shortcrested) freak waves are simulated experimentally through the dispersive and directional focusing of component waves, and the wavelengths obtained from the surface elevations measured by the wave gauge array are compared with the results from the linear, 3rd-order and 5th-order Stokes wave theories. The comparison results suggest that the 3rd-order theory estimates the wavelengths of freak waves with higher accuracy than the linear and 5th-order theories. Furthermore, the results allow insights into the dominant factors. It is particularly noteworthy that the accuracy is likely to depend on the wave period, and that the wavelengths of longer period freak waves are overestimated but the wavelengths are underestimated for shorter period ones. In order to decrease the deviation, a modified formulation is presented to predict the wavelengths of two-and three-dimensional freak waves more accurately than the 3rd-order dispersion relation, by regression analysis. The normalized differences between the predicted and experimental results are over 50% smaller for the modified model suggested in this study compared with the 3rd-order dispersion relation.

关键词： freak wave rogue wave wavelength three-dimension directional spread multidirectional wave

用Hirota双线性导数变换求MNLS方程的rogue波解

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数学物理学报（A辑） 2023年第1期43卷 132-142页

作者：唐宇轩周国全武汉大学物理科学与技术学院武汉430072

修正的非线性薛定谔方程(MNLS方程)与导数非线性薛定谔方程(DNLS方程)是两个紧密相关且完全可积的非线性偏微分方程.该文通过Hirota双线性导数变换方法,首先求得MNLS方程在平面简谐波背景下的空间周期解,即Akhmediev型呼吸子解,再通过... 详细信息

修正的非线性薛定谔方程(MNLS方程)与导数非线性薛定谔方程(DNLS方程)是两个紧密相关且完全可积的非线性偏微分方程.该文通过Hirota双线性导数变换方法,首先求得MNLS方程在平面简谐波背景下的空间周期解,即Akhmediev型呼吸子解,再通过长波极限得其rogue波解.根据简单的参数归零法使之自然地约化为DNLS方程的rogue波解,并借助于一个积分变换将其变换为Chen-Lee-Liu方程的rogue波解.文章还简要讨论了MNLS方程和DNLS方程在非局域情形整体解的存在性问题.

关键词： rogue wave MNLS方程 DNLS方程 Hirota双线性导数变换空间周期解呼吸子解