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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 method.In 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 N-solitons.Besides the fundamental pattern of rogue waves,the triangle or pentagon patterns are also obtained.Moreover,the different patterns of these solutions are determined by newly introduced parameters.In 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

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

Estimating the evolution of sea state non-Gaussianity based on a phase-resolving model

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Journal of Oceanology and Limnology 2022年第5期40卷 1909-1923页

作者： Xingjie JIANG Tingting ZHANG Dalu GAO Daolong WANG Yongzeng YANG First Institute of Oceanography and Key Laboratory of Marine Science and Numerical ModelingMinistry of Natural ResourcesQingdao 266061China Laboratory for Regional Oceanography and Numerical Modeling Pilot National Laboratory for Marine Science and Technology(Qingdao)Qingdao 266237China Shandong Key Laboratory of Marine Science and Numerical Modeling Qingdao 266061China Ocean University of China College of Oceanic and Atmospheric SciencesQingdao 266071China

The occurrence of rogue waves is closely related to the non-Gaussianity of sea states,and this non-Gaussianity can be estimated using corresponding two-dimensional wave spectra.This paper presents an approach to non-Gaussianity estimation based on a phase-resolving model called the high-order spectral method(HOSM).Based on numerous HOSM simulations,a set of precalculated non-Gaussianity indicators was established that could be applied to real sea states without any calibration of spectral shapes.With a newly developed extraction approach,the indicators for given two-dimensional wave spectra could then be conveniently extracted from the precalculated dataset.The feasibility of the newly developed approach in a real wave environment is verified.Using the estimation approach,phase-resolved non-Gaussianity can now be illustrated throughout the evolution of sea states of interest,not just at a few specific times;and the level of non-Gaussianity at any time in a duration can be identified according to the statistics(e.g.,quantities)of the phase-resolved indicators,that are obtained throughout the duration concerned.

关键词： rogue wave sea state non-Gaussianity high-order spectral method spectral geometry wave-wave nonlinearity

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 method.We 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 quickly.We 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 wave.Furthermore,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

Nonlinear waves of the Hirota and the Maxwell Bloch equations in nonlinear optics

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Chinese Physics B 2013年第4期22卷 292-301页

作者：李传忠贺劲松 K. Porseizan Department of Mathematics Ningbo University Department of Physics Pondicherry University Institute of Condensed Matter Theory and Solid State Optics Friedrich-Schiller-Universitt Jena Max-Wein Platz 1 D-07743 Jena Germany

In this paper, considering the Hirota and the Maxwell–Bloch （H-MB） equations which are governed by femtosecond pulse propagation through a two-level doped fiber system, we construct the Darboux transformation of this system through a linear eigenvalue problem. Using this Daurboux transformation, we generate multi-soliton, positon, and breather solutions （both bright and dark breathers） of the H-MB equations. Finally, we also construct the rogue wave solutions of the above system.

关键词： Hirota and Maxwell–Bloch equations nonlinear optics rogue wave

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 equations.Our 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 term.We also obtain the analytical transformation from the initial seed solution to unique rogue waves with the bountiful pair structure.In a special case,the asymmetry rogue wave can own the spatial and temporal symmetry gradually,which is controlled by one parameter.It 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

Inverse scattering transforms of the inhomogeneous fifth-order nonlinear Schrodinger equation with zero/nonzero boundary conditions

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Communications in Theoretical Physics 2022年第8期74卷 56-68页

作者： Jin-Jin Mao Shou-Fu Tian Tian-Zhou Xu Lin-Fei Shi School of Mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China School of Mathematics China University of Mining and TechnologyXuzhou 221116China

The present work studies the inverse scattering transforms(IST)of the inhomogeneous fifth-order nonlinear Schrodinger(NLS)equation with zero boundary conditions(ZBCs)and nonzero boundary conditions(NZBCs).Firstly,the bound-state solitons of the inhomogeneous fifth-order NLS equation with ZBCs are derived by the residue theorem and the Laurent's series for the first time.Then,by combining with the robust IST,the Riemann-Hilbert(RH)problem of the inhomogeneous fifth-order NLS equation with NZBCs is revealed.Furthermore,based on the resulting RH problem,some new rogue wave solutions of the inhomogeneous fifth-order NLS equation are found by the Darboux transformation.Finally,some corresponding graphs are given by selecting appropriate parameters to further analyze the unreported dynamic characteristics of the corresponding solutions.

关键词： the inhomogeneous fifth-order nonlinear Schrodinger equation inverse scattering transforms Darboux transformation bound-state soliton rogue wave zero/nonzero boundary conditions

Theoretical Approximation of Focusing-wave Induced Load upon A Large-Scale Vertical Cylinder

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China Ocean Engineering 2017年第5期31卷 598-606页

作者： XUE Hong-xiang HU Zhe TANG Wen-yong ZHANG Xiao-ying WANG Kun-peng State Key Laboratory of Ocean Engineering Shanghai Jiao Tong University Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration Key Laboratory of Ships and Ocean Engineering of Fujian Province Jimei University School of Naval Architecture and Ocean Engineering Jiangsu University of Science and Technology

Until now, most researches into the rogue-wave-structure interaction have relied on experimental measurement and numerical simulation. Owing to the complexity of the physical mechanism of rogue waves, theoretical study on the wave-structure issue still makes little progress. In this paper, the rogue wave flow around a vertical cylinder is analytically studied within the scope of the potential theory. The rogue wave is modeled by the Gauss envelope, which is one particular case of the well-known focusing theory. The formulae of the wave-induced horizontal force and bending moment are proposed. For the convenience of engineering application, the derived formulae are simplified appropriately, and verified against numerical results. In addition, the influence of wave parameters, such as the energy focusing degree and the wave focusing position, is thoroughly investigated.

关键词： rogue wave Gauss envelope upright cylinder potential theory analytical approximation