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1.
基于sl(4,(C))的loop代数的非平凡李代数分裂,构造了5类新的孤子方程族.这些代数分裂通过构造从正李子代数到负李子代数的线性箅子B统一得到.对所有可能的线性箅子B进行分类,证明存在5类4×4仿射B-型KdV方程族.利用Adler- Konstant- Symes理论获得了这些方程族的Hamilton结构,并利用loop群方法得到其B(a)cklund变换. 相似文献
2.
New Solitary Solutions of (2+1)-Dimensional Variable Coefficient Nonlinear Schrodinger Equation with an External Potential 下载免费PDF全文
By a series of transformations, the (2+1)-dimensional variable coefficient nonlinear Schr?dinger equation can turn to the Klein-Gordon equation. Many new double travelling wave solutions of the Klein-Gordon equation are obtained. Thus, the new solitary solutions of the variable coefficient nonlinear Schr?inger equation with an external potential can be found. 相似文献
3.
本文主要从孤子、混沌、分形理论以及神经网络这4个方面讨论了非线性科学的主要特点与重要应用, 并结合实例说明在力学问题研究中的应用. 相似文献
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以中国传统文化为底蕴、机械化和道理化为特色的中国传统数学,曾经取得光辉的成就.将这些思想用于计算机科学、孤子理论和量子场论,不仅可以系统地产生已有结果,还可以开辟新的研究方向,取得重大突破. 相似文献
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Self-adjoint theorem is introduced to match the corresponding functional of the given differential equations,and then Noether's theorem is used to determine the extended conservation laws of the original equations. Finally, as the application of the method, the conservation laws of Drinfel'd-Sokolov-Wilson equation and Benjamin-Bona-Mahony equation are constructed. 相似文献
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该文基于一个Riccati方程组,提出了一个新的广义投影Ric cati展开法,该方法直接简单并能构造非线性微分方程更多的新的解析解。利用该算法研究了(2+1)维广义浅水波方程,并求得了许多新的精确解,包括类孤子解和周期解。该算法也能应用到其它非线性微分方程中。 相似文献
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In this paper, we obtain the linear differential conditions of (3 + 1)-dimensional Jimbo-Miwa equation and Boiti-Leon-Manna-Pempinelli equation, which guarantee that the corresponding Wronskian determinant solves the two equations in the Hirota bilinear form. By using the properties of Young diagram, we have proved the results. 相似文献
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本文立足于中国传统文化提出非线性学习方法, 使数学物理中国化、简单化、个性化. 从八卦的角度统一看待非线性科学中的孤子、混沌、分形和机器学习, 以诗联网引领学科之间的对话, 实现学科之间的乾坤大挪移. 相似文献
9.
Lie symmetry reduction of some truly "variable coefficient" wave equations which are singled out from a class of (1 + 1)-dimensional variable coefficient nonlinear wave equations with respect to one and two-dimensional algebras is carried out. Some classes of exact solutions of the investigated equations are found by means of both the reductions and some modern techniques such as additional equivalent transformations and hidden symmetries and so on. Conditional symmetries are also discussed. 相似文献
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