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广义的Hirota-Satsuma耦合KdV系统的精确行波解(英文) 被引量:1
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作者 王晓民 苏道毕力格 《内蒙古工业大学学报(自然科学版)》 2013年第1期6-10,共5页
本文借助于计算机代数系统Mathematica,利用(G'/G)-展开法成功获得了广义的Hirota-Satsuma耦合KdV系统丰富的精确行波解,并且分别以含两个任意参数的双曲函数、三角函数及有理函数等三种形式表示.
关键词 (G' G)-展开法 精确行波解 广义的Hirota-Satsuma耦合kdv系统
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耦合KdV系统中的孤子——混沌跃迁
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作者 海文华 《湘潭师范学院学报(自然科学版)》 2002年第3期1-7,共7页
讨论了两个具有任意非零散射多数的弱耦合KdV方程 ,得到了初始常数和系统参数间的某些关系。结果表明 :在孤子和混沌间存在着跃迁 ,并证明了控制跃迁的方法适用于控制参数的调节关系。
关键词 耦合kdv系统 孤子 混沌跃迁 初始常数 系统参数 非零散射
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耦合mKdV系统的非奇异正子解、负子解及复子解 被引量:4
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作者 张玲 桑本文 胡恒春 《上海理工大学学报》 CAS 北大核心 2012年第1期76-80,87,共6页
研究从二层流体模型中导出的变系数耦合mKdV模型,利用达布变换法,并依据系统中Lax对的谱参数的性质,给出了耦合mKdV系统的正子解、负子解、复子解及这些解的具体结构图形.其中所得到的耦合mKdV系统的正子解、负子解和复子解都是解析的,... 研究从二层流体模型中导出的变系数耦合mKdV模型,利用达布变换法,并依据系统中Lax对的谱参数的性质,给出了耦合mKdV系统的正子解、负子解、复子解及这些解的具体结构图形.其中所得到的耦合mKdV系统的正子解、负子解和复子解都是解析的,而复子解可看作一种形式的周期波解. 展开更多
关键词 正子解 负子解 复子解 耦合kdv系统
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Coupled KdV Equations and Their Explicit Solutions Through Two-Dimensional Hamiltonian System with a Quartic Potential 被引量:1
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作者 CAO Jian-Li ZHANG Hua JIAO Wan-Tang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第6期1379-1382,共4页
Based on the second integrable ease of known two-dimensional Hamiltonian system with a quartie potentiM, we propose a 4 × 4 matrix speetrM problem and derive a hierarchy of coupled KdV equations and their Hamilto... Based on the second integrable ease of known two-dimensional Hamiltonian system with a quartie potentiM, we propose a 4 × 4 matrix speetrM problem and derive a hierarchy of coupled KdV equations and their Hamiltonian structures. It is shown that solutions of the coupled KdV equations in the hierarchy are reduced to solving two compatible systems of ordinary differentiM equations. As an application, quite a few explicit solutions of the coupled KdV equations are obtained via using separability for the second integrable ease of the two-dimensional Hamiltonian system. 展开更多
关键词 coupled kdv equations integrable system explicit solution
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Higher-Dimensional Lie Algebra and New Integrable Coupling of Discrete KdV Equation
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作者 李欣越 宋宏伟 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第7期7-15,共9页
Based on semi-direct sums of Lie subalgebra G, a higher-dimensional 6 × 6 matrix Lie algebra sμ(6) is constructed. A hierarchy of integrable coupling KdV equation with three potentials is proposed, which is de... Based on semi-direct sums of Lie subalgebra G, a higher-dimensional 6 × 6 matrix Lie algebra sμ(6) is constructed. A hierarchy of integrable coupling KdV equation with three potentials is proposed, which is derived from a new discrete six-by-six matrix spectral problem. Moreover, the Hamiltonian forms is deduced for lattice equation in the resulting hierarchy by means of the discrete variational identity -- a generalized trace identity. A strong symmetry operator of the resulting hierarchy is given. Finally, we prove that the hierarchy of the resulting Hamiltonian equations is Liouville integrable discrete Hamiltonian systems. 展开更多
关键词 semi-direct sums of Lie subalgebra integrable couplings discrete variational identity Liouvilleintegrability
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A Coupled Hybrid Lattice: Its Related Continuous Equation and Symmetries 被引量:1
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作者 刘萍 付培凯 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第7期5-10,共6页
The hybrid lattice, known as a discrete Korteweg-de Vries (KdV) equation, is found to be a discrete modified Korteweg-de Vries (mKdV) equation in this paper. The coupled hybrid lattice, which is pointed to be a discre... The hybrid lattice, known as a discrete Korteweg-de Vries (KdV) equation, is found to be a discrete modified Korteweg-de Vries (mKdV) equation in this paper. The coupled hybrid lattice, which is pointed to be a discrete coupled KdV system, is also found to be discrete form of a coupled mKdV systems. Delayed differential reduction system and pure difference systems are derived from the coupled hybrid system by means of the symmetry reduction approach. Cnoidal wave, positon and negaton solutions for the coupled hybrid system are proposed. 展开更多
关键词 coupled hybrid lattice SYMMETRIES discrete kdv equation
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Bell Polynomial Approach and N-Soliton Solutions for a Coupled KdV-mKdV System 被引量:1
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作者 覃翌 高以天 +1 位作者 于鑫 蒙高庆 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第7期73-78,共6页
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 Bel... 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. 展开更多
关键词 coupled kdv-modified kdv system bilinear form N-soliton solutions binary Bell polynomials symbolic computation soliton interaction
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