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Exact Solutions to a (3+1)-Dimensional Variable-Coefficient Kadomtsev-Petviashvilli Equation via the bilinear Method and Wronskian Technique

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Communications in Theoretical Physics 2009年第9期52卷 468-472页

作者： ZHANG Chcng TIAN Bo XU Tao LI Li-Li Lü Xing GENG Tao ZHU Hong-Wu School of Science P.O. Box 122 Beijing University of Posts and Telecommunications Beijing 100876 China State Key Laboratory of Software Development Environment Beijing University of Aeronautics and Astronautics Beijing 100191 China Key Laboratory of Information Photonics and Optical Communications Ministry of Education Beijing University of Posts and Telecommunications Beijing 100876 China

By truncating the Painleve expansion at the constant level term,the Hirota bilinear form is obtainedfor a (3+1)-dimensional variable-coefficient Kadomtsev-Petviashvili *** on its bilinear form,solitary-wavesolutions are constructed via the ε-expansion method and the corresponding graphical analysis is ***,the exact solution in the Wronskian form is presented and proved by direct substitution into the bilinear equation.

关键词： (3+1)-dimensional variable-coefficient Kadomtsev-Petviashvili equation Wronskian solution bilinear form exact solution

New Double-Periodic Soliton Solutions for the (2+1)-Dimensional Breaking Soliton Equation

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Communications in Theoretical Physics 2018年第5期69卷 585-597页

作者：刘建国田玉 School of Science Beijing University of Posts and Telecommunications School of automation Beijing University of Posts and Telecommunications College of Computer Jiangxi University of Traditional Chinese Medicine

Under investigation is the(2+1)-dimensional breaking soliton equation. Based on a special ans?tz functions and the bilinear form, some entirely new double-periodic soliton solutions for the(2+1)-dimensional breaking soliton equation are presented. With the help of symbolic computation software Mathematica, many important and interesting properties for these obtained solutions are revealed with some figures.

关键词： bilinear form special ansatz functions (2+1)-dimensional breaking soliton equation symbolic computation

On the bilinear and Cubic forms of Some Symplectic Connected Sums

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Acta Mathematica Sinica,English Series 2012年第9期28卷 1809-1822页

作者： Wei WANG School of Mathematical Sciences Fudan University

Let （M1, M2, N） be three symplectic manifolds and suppose that we can do the symplectic connected sum of M1 and M2 along their submanifold N to obtain M1^#NM2. In this paper, we consider the bilinear and cubic forms of H＊（M1^#NM2, Z） when dimM1^#NM2 = 4, 6. Under some conditions, we get some relations of the bilinear and the cubic forms between M1^#NM2 and M1 [I Ms.

关键词： Symplectic connected sum cohomology bilinear form cubic form

Painleve Analysis and Determinant Solutions of a (3+1)-Dimensional Variable-Coefficient Kadomtsev-Petviashvili Equation in Wronskian and Grammian form

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Communications in Theoretical Physics 2009年第6期51卷 1062-1068页

作者： MENG Xiang-Hua TIAN Bo FENG Qian YAO Zhen-Zhi GAO Yi-Tian School of Science P.O. Box 122 Beijing University of Posts and Telecommunications Beijing 100876 China State Key Laboratory of Software Development Environment Beijing University of Aeronautics and Astronautics Beijing 100191 China Key Laboratory of Information Photonics and Optical Communications Ministry of Education Beijing University of Posts and Telecommunications Beijing 100876 China Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics Beijing University of Aeronautics and Astronautics Beijing 100191 China

In this paper, the investigation is focused on a （3＋1）-dimensional variable-coefficient Kadomtsev- Petviashvili （vcKP） equation, which can describe the realistic nonlinear phenomena in the fluid dynamics and plasma in three spatial dimensions. In order to study the integrability property of such an equation, the Painlevé analysis is performed on it. And then, based on the truncated Painlevé expansion, the bilinear form of the （3＋1）-dimensionaJ vcKP equation is obtained under certain coefficients constraint, and its solution in the Wronskian determinant form is constructed and verified by virtue of the Wronskian technique. Besides the Wronskian determinant solution, it is shown that the （3＋1）-dimensional vcKP equation also possesses a solution in the form of the Grammian determinant.

关键词： (3+1)-dimensional variable-coefficient Kadomtsev-Petviashvili equation Painlev@ analysis bilinear form Wronskian determinant Grammian determinant symbolic computation

New Exact Periodic Solitary-Wave Solutions for New (2+1)-Dimensional KdV Equation

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Communications in Theoretical Physics 2009年第11期52卷 862-864页

作者： WANG Chuan-Jia DAI Zheng-De MU Gui LIN Song-Qing School of Mathematics and Statistics Yunnan University Kunming 650091 China

The extended homoclinic test function method is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations. In this paper, with the help of this approach, we obtain new exact solutions （including kinky periodic solitary-wave solutions, periodic soliton solutions, and cross kink-wave solutions） for the new （2＋1）-dimensional KdV equation. These results enrich the variety of the dynamics of higher-dimensionai nonlinear wave field.

关键词： kinky wave solution periodic soliton solution extended homoclinic test function method KdV equation bilinear form

Generalized Wronskian Solutions to Modified Korteweg-de Vries Equation via Its Bcklund Transformation

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Communications in Theoretical Physics 2008年第7期50卷 13-16页

作者： XUAN Qi-Fei ZHANG Da-Jun Department of Mathematics Shanghai University Shanghai 200444 China

In the paper we discuss the Wronskian solutions of modified Korteweg-de Vries equation （mKdV） via the Backlund transformation （BT） and a generalized Wronskian condition is given, which allows us to substitute an a... 详细信息

关键词： the modified Korteweg-de Vries equation (mKdV) generalized Wronskian solutions bilinear form Backlund transformation (BT)

Bell Polynomial Approach and N-Soliton Solutions for a Coupled KdV-mKdV System

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Communications in Theoretical Physics 2012年第7期58卷 73-78页

作者：覃翌高以天于鑫蒙高庆 Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics Beijing University of Aeronautics and Astronautics State Key Laboratory of Software Development Environment Beijing University of Aeronautics and Astronautics

In fluid dynamics, plasma physics and nonlinear optics, Korteweg-de Vries (KdV)-type equations are used to describe certain phenomena. In this paper, a coupled KdV-modified KdV system is investigated. Based on the Bell polynomials and symbolic computation, the bilinear form of such system is derived, and its analytic N-soliton solutions are constructed through the Hirota method. Two types of multi-soliton interactions are found, one with the reverse of solitonic shapes, and the other, without. Both the two types can be considered elastic. For a pair of solutions to such system, u and v, with the number of solitons N even, the soliton shapes of u stay unvaried while those of v reverse after the interaction; with N odd, the soliton shapes of both u and v keep unchanged after the interaction.

关键词： coupled KdV-modified KdV system bilinear form N-soliton solutions binary Bell polynomials symbolic computation soliton interaction

Casoratian Solutions to Toda Lattice Via Its Backlund Transformation

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Communications in Theoretical Physics 2010年第3期53卷 435-439页

作者：玄其飞张大军周静 Department of Mathematics Shanghai University

Generalized Casoratian condition and Casoratian solutions of the Toda lattice are given in terms of its bilinear Bgcklund transformation. By choosing suitable Casoratian entries and parameter in the bilinear Bgcklund ... 详细信息

关键词： Toda lattice Casoratian solution bilinear form Backlund transformation

Multiple rational rogue waves for higher dimensional nonlinear evolution equations via symbolic computation approach

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Journal of Ocean Engineering and Science 2023年第1期8卷 33-41页

作者： Saima Arshed Nauman Raza Asma Rashid Butt Ahmad Javid J.F.Gómez-Aguilar Department of Mathematics University of the PunjabQuaid-e-Azam CampusLahorePakistan Department of Mathematics University of Engineering and TechnologyLahorePakistan School of Natural Sciences(SNS) National University of Sciences and Technology(NUST)Islamabad 44000Pakistan CONACyT-Tecnológico Nacional de México/CENIDET Interior Internado Palmira S/NCol.PalmiraCuernavaca Morelos C.P.62490México

The paper investigates the multiple rogue wave solutions associated with the generalized Hirota-Satsuma-Ito(HSI)equation and the newly proposed extended(3+1)-dimensional Jimbo-Miwa(JM)equation with the help of a symbolic computation *** incorporating a direct variable trans-formation and utilizing Hirota’s bilinear form,multiple rogue wave structures of different orders are ob-tained for both generalized HSI and JM *** obtained bilinear forms of the proposed equations successfully investigate the 1st,2nd and 3rd-order rogue *** constructed solutions are verified by inserting them into original *** computations are assisted with 3D graphs to analyze the propagation dynamics of these rogue *** properties of these waves are governed by different parameters that are discussed in details.

关键词： Generalized Hirota-Satsuma-Ito(HSI) equation The new extended(3+1)-dimensional Jimbo-Miwaequation Symbolic computation approach bilinear form Rogue wave solutions