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High-order rational solutions and resonance solutions for a (3+1)-dimensional Kudryashov–Sinelshchikov equation

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Chinese Physics B 2021年第1期30卷 134-141页

作者：岳云飞林机陈勇 School of Mathematical Sciences Shanghai Key Laboratory of PMMPShanghai Key Laboratory of Trustworthy ComputingEast China Normal UniversityShanghai 200062China Department of Physics Zhejiang Normal UniversityJinhua 321004China College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590China

We mainly investigate the rational solutions and N-wave resonance solutions for the(3+1)-dimensional Kudryashov–Sinelshchikov equation, which could be used to describe the liquid containing gas bubbles. With appropriate transformations, two kinds of bilinear forms are derived. Employing the two bilinear equations, dynamical behaviors of nine district solutions for this equation are discussed in detail, including bright rogue wave-type solution, dark rogue wave-type solution, bright W-shaped solution, dark W-shaped rational solution, generalized rational solution and bright-fusion, darkfusion, bright-fission, and dark-fission resonance solutions. In addition, the generalized rational solutions, which depending on two arbitrary parameters, have an interesting structure: splitting from two peaks into three peaks.

关键词： rational solution N-wave resonance solution Hirota bilinear method Kudryashov–Sinelshchikov equation

Linear superposition of Wronskian rational solutions to the KdV equation

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Communications in Theoretical Physics 2021年第6期73卷 1-5页

作者： Wen-Xiu Ma Department of Mathematics Zhejiang Normal UniversityJinhua 321004ZhejiangChina Department of Mathematics King Abdulaziz UniversityJeddah 21589Saudi Arabia Department of Mathematics and Statistics University of South FloridaTampaFL 33620-5700United States of America School of Mathematical and Statistical Sciences North-West UniversityMafikeng CampusPrivate Bag X2046Mmabatho 2735South Africa

A linear superposition is studied for Wronskian rational solutions to the Kd V equation,which include rogue wave *** is proved that it is equivalent to a polynomial identity that an arbitrary linear combination of two Wronskian polynomial solutions with a difference two between the Wronskian orders is again a solution to the bilinear Kd V *** is also conjectured that there is no other rational solutions among general linear superpositions of Wronskian rational solutions.

关键词： soliton equation Wronskian solution rational solution rogue wave the KdV equation

Some Results on Difference Riccati Equations

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Acta Mathematica Sinica,English Series 2011年第6期27卷 1091-1100页

作者： Zong Xuan CHEN Kwang Ho SHON School of Mathematical Sciences South China Normal University Guangzhou 510631 P. R. China Department of Mathematics College of Natural Sciences Pusan National University Pusan 609-735 Korea

Some properties of solutions for the difference Riccati equations are obtained. The existence and forms of rational solutions, and the Borel exceptional value, zeros, poles and fixed points of transcendental solutions... 详细信息

关键词： Difference Riccati equation rational solution transcendental solution Borel exceptionalvalue

STUDY ON EXACT ANALYTICAL solutionS FOR TWO SYSTEMS OF NONLINEAR EVOLUTION EQUATIONS

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Applied Mathematics and Mechanics(English Edition) 2001年第8期22卷 925-934页

作者： YAN Zhen-ya(闫振亚) ZHANG Hong-qing(张鸿庆) Department of Applied Mathematics Dalian University of Technology Dalian 116024 P R China Department of Applied Mathematics Dalian University of Technology Dalian 116024 P R China

The homogeneous balance method was improved and applied to two systems Of nonlinear evolution equations. As a result, several families of exact analytic solutions are derived by some new ansatzs. These solutions contain Wang's and Zhang's results and other new types of analytical solutions, such as rational fraction solutions and periodic solutions. The way can also be applied to solve more nonlinear partial differential equations.

关键词： nonlinear evolution equations improved homogeneous balance method exact analytical solution solitary wave solution rational solution

符号计算与非线性偏微分方程精确行波解(英文)

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Journal of Shanghai University(English Edition) 2008年第6期12卷 481-485页

作者：吴国成夏铁成 Department of Mathematics College of Sciences Shanghai University Key Laboratory of Mathematics Mechanization Chinese Academy of Science

In this paper, with the aid of the symbolic computation, a further extended tanh function method was presented. Based on the new general ansatz, many nonlinear partial differential equation（s）（NPDE（s）） can he solved. Especially, as applications, a compound KdV-mKdV equation and the Broer-Kaup equations are considered successfully, and many solutions including periodic solutions, triangle solutions, and rational solutions are obtained. The method can also be applied to other NPDEs.

关键词： nonlinear partial differential equations (NPDEs) rational solution soliton solution doubly periodic solution Wu method

New Exact Traveling Wave solutions to（2+1）-Dimensional GMKPI Equation

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New Exact Traveling Wave Solutions to（2+1）-Dimensional GMK...