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Investigation on the resonance phenomena of multi-solitons for the (3+1)-dimensional kadomtsev-petviashvili equation

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Chinese Physics B 2011年第1期20卷 473-478页

作者：石玉仁张娟杨红娟段文山 Karl E.Lonngren College of Physics and Electronic Engineering Northwest Normal University Department of Electrical and Computer Engineering The University of IowaIowa CityIA 52242USA

In this paper, we theoretically investigate the four-soliton interaction and their resonance phenomena of the （3＋1）- dimensional kadomtsev petviashvili （KP） equation. We find that the maximum amplitude of the resonantly created soliton can be 16 times that of one of the four equi-amplitude initial interacting solitons. We also find that the maximum amplitude can only be 4 times the initial soliton amplitude when the resonance phenomena does not take place. The case of four solitons with different amplitudes also has been studied analytically. The results indicate that the resonance phenomena still exists in this case. Numerical results confirm the theoretical predictions.

关键词： kadomtsev-petviashvili equation soliton resonance

New interaction solutions of the kadomtsev–petviashvili equation

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Chinese Physics B 2014年第10期23卷 1-6页

作者：刘希忠俞军任博杨建荣 Institute of Nonlinear Science Shaoxing University Department of Physics and Electronics Shangrao Normal University

The residual symmetry relating to the truncated Painlev6 expansion of the kadomtsev-petviashvili （KP） equation is nonlocal, which is localized in this paper by introducing multiple new dependent variables. By using the standard Lie group approach, new symmetry reduction solutions for the KP equation are obtained based on the general form of Lie point symmetry for the prolonged system. In this way, the interaction solutions between solitons and background waves are obtained, which are hard to find by other traditional methods.

关键词： kadomtsev-petviashvili equation localization procedure residual symmetry Baicklund transfor-mation symmetry reduction solution

The D’Alembert type waves and the soliton molecules in a (2+1)-dimensional kadomtsev-petviashvili with its hierarchy equation

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Communications in Theoretical Physics 2021年第10期73卷 14-22页

作者： Hui-Ling Wu Sheng-Wan Fan Jin-Xi Fei Zheng-Yi Ma Institute of Nonlinear Analysis and Department of Mathematics Lishui UniversityLishui 323000China Institute of Optoelectronic Technology and Department of Photoelectric Engineering Lishui UniversityLishui 323000China Department of Mathematics Zhejiang Sci-Tech UniversityHangzhou 310018China

For a one(2+1)-dimensional combined kadomtsev-petviashvili with its hierarchy equation, the missing D’Alembert type solution is derived first through the traveling wave transformation which contains several special kink molecule structures. Further, after introducing the B?cklund transformation and an auxiliary variable, the N-soliton solution which contains some soliton molecules for this equation, is presented through its Hirota bilinear form. The concrete molecules including line solitons, breathers and a lump as well as several interactions of their hybrid are shown with the aid of special conditions and parameters. All these dynamical features are demonstrated through the different figures.

关键词： kadomtsev-petviashvili equation soliton molecule breather/lump soliton elastic interaction

New solitary wave structures to the(3+1)dimensional kadomtsev-petviashvili and Schrödinger equation

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Journal of Ocean Engineering and Science 2019年第4期4卷 373-378页

作者： Hasan Bulut Emine Nesligül Aksan MiraçKayhan Tukur Abdulkadir Sulaıman Department of Mathematics University of FıratElazıgTurkey Department of Mathematics University of InonuMalatyaTurkey Department of Mathematics Federal University DutseJigawaNigeria

The studies of the dynamic behaviors of nonlinear models arising in ocean engineering play a significant role in our daily *** this paper,an efficient mathematical technique,namely;the sine-Gordon expansion method is employed to construct the traveling wave solutions to the(3+1)-dimensional kadomtsev-petviashvili and(3+1)-dimensional nonlinear Schrödinger *** suitable values of the parameters,the two-and three-dimensional figures of the obtained solutions are plotted.

关键词： Sine-Gordon expansion method kadomtsev-petviashvili equation Schrödinger equation wave solutions

Modified (2+1)-dimensional displacement shallow water wave system and its approximate similarity solutions

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Chinese Physics B 2011年第9期20卷 30-36页

作者：刘萍付培凯 Department of Electronic Engineering University of Electronic Science and Technology of China Zhongshan Institute Academic Affairs Division Zhongshan Polytechnic

Recently, a new （2＋1）-dimensional shallow water wave system, the （2＋1）-dlmenslonal displacement shallow water wave system （2DDSWWS）, was constructed by applying the variational principle of the analytic mechanics in the Lagrange coordinates. The disadvantage is that fluid viscidity is not considered in the 2DDSWWS, which is the same as the famous kadomtsev-petviashvili equation and Korteweg-de Vries equation. Applying dimensional analysis, we modify the 2DDSWWS and add the term related to the fluid viscidity to the 2DDSWWS. The approximate similarity solutions of the modified 2DDSWWS （M2DDSWWS） is studied and four similarity solutions are obtained. For the perfect fluids, the coefficient of kinematic viscosity is zero, then the M2DDSWWS will degenerate to the 2DDSWWS.

关键词： modified (2+1)-dimensional displacement shallow water wave system viscidity approx-imate similarity solutions kadomtsev-petviashvili equation

Multisoliton Solutions for the Isospectral and Nonisospectral BKP equation with Self-Consistent Sources

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Chinese Physics Letters 2008年第7期25卷 2331-2334页

作者：邓淑芳 Department of Mathematics East China University of Science and Technology Shanghai 200237

The isospectral and nonisospectral BKP equation with self-consistent sources is derived to study the linear problem of the BKP system. The bilinear form of the nonisospeetral BKP equation with self-consistent sources ... 详细信息

关键词： kadomtsev-petviashvili equation NONLINEAR INTEGRABLE SYSTEMS WAVES HIERARCHY SOLITONS

Stable-range Approach to the （2＋1）-dimensional Breaking Soliton and kadomtsev-petviashvili equations

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Chinese Quarterly Journal of Mathematics 2012年第2期27卷 183-190页

作者： ZHANG Ying LI Ji-na ZHA NG Jiang-hong SONG Xiao-qian Department of Mathematics Northwest University Xi'an 710069 China College of Science Zhongyuan University of Technology Zhengzhou 450007 China Department of Physical Education Tianshui Normal University Tianshui 741001 China School of Mathematics and Statistics Chongqing Three Gorges University Chongqing 404199 China

By using Xu's stable-range method,families of explicit exact solutions with multiple parameter functions for the(2+1)-dimensional breaking soliton and kadomtsevpetviashvili *** parameter functions make our solutions m... 详细信息

关键词： exact solutions breaking soliton equation kadomtsev-petviashvili equation Stable-range

Wave profile analysis of a couple of(3+1)-dimensional nonlinear evolution equations by sine-Gordon expansion approach

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Journal of Ocean Engineering and Science 2022年第3期7卷 272-279页

作者： Md.Rezwan Ahamed Fahim Purobi Rani Kundu Md.Ekramul Islam M.Ali Akbar M.S.Osman Department of Mathematics Pabna University of Science and TechnologyBangladesh Department of Applied Mathematics University of RajshahiBangladesh Department of Mathematics Faculty of ScienceCairo UniversityGiza 12613Egypt Department of Mathematics Faculty of Applied ScienceUmm Alqura UniversityMakkah 21955Saudi Arabia

The(3+1)-dimensional kadomtsev-petviashvili and the modified KdV-Zakharov-Kuznetsov equations have a significant impact in modern science for their widespread applications in the theory of long-wave propagation,dynamics of shallow water wave,plasma fluid model,chemical kinematics,chemical engineering,geochemistry,and many other *** this article,we have assessed the effects of wave speed and physical parameters on the wave contours and confirmed that waveform changes with the variety of the free factors in *** a result,wave solutions are extensively analyzed by using the balancing condition on the linear and nonlinear terms of the highest order and extracted different standard wave configurations,containing kink,breather soliton,bell-shaped soliton,and periodic *** extract the soliton solutions of the high-dimensional nonlinear evolution equations,a recently developed approach of the sine-Gordon expansion method is used to derive the wave solutions *** sine-Gordon expansion approach is a potent and strategic mathematical tool for instituting ample of new traveling wave solutions of nonlinear *** study established the efficiency of the described method in solving evolution equations which are nonlinear and with higher dimension(HNEEs).Closed-form solutions are carefully illustrated and discussed through diagrams.

关键词： Sine-Gordon expansion approach kadomtsev-petviashvili equation modified KdV-Zakharov-Kuznetsov equation soliton solutions

Periodic Wave Solution to the （3＋1）-Dimensional Boussinesq equation

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Chinese Physics Letters 2008年第8期25卷 2739-2742页

作者：吴勇旗 Department of Mathematics Zhanjiang Normal University Zhanjiang 524048

One- and two-periodic wave solutions for （3＋l）-dimensional Boussinesq equation are presented by means of Hirota＇s bilinear method and the Riemann theta function. The soliton solution can be obtained from the perio... 详细信息

关键词： kadomtsev-petviashvili equation ELLIPTIC FUNCTION EXPANSION