Symmetries and similarity reductions of the dym equation

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	Symmetries and similarity reductions of the dym equation
	Lou, SY; Lou, SY , NINGBO NORMAL COLL,INST MODERN PHYS,NINGBO 315211,PEOPLES R CHINA.
刊名	PHYSICA SCRIPTA
	1996
卷号	54 期号:5 页码:428-435
关键词	Partial-differential Equations Dym Korteweg-devries Hierarchy Harry Linear Evolution-equations Sawada-kotera Equation Recursion Operator Painleve Property Discrete Eigenfunctions Singularity Analysis Kdv Equation
ISSN号	0281-1847
英文摘要	The eigenfunctions of the recursion operator Phi with eigenvalue lambda(i), and the inverse of the recursion operator Phi(i) = Phi - lambda(i) for the Dym equation (DE) are obtained by means of the pseudopotentials or the isospectral functions of the isospectral problem. The symmetries and algebras of the DE are also given. Using some symmetry subalgebra of the DE, thirteen types of the significant similarity reductions are obtained by virtue of the classical Lie approach. For six types of reductions, the general solutions can be obtained by means of the Weierstrass elliptic function, Riemann's zeta function, Jacobi elliptic functions and the solutions of a Riccati equation implicitly. Three types of reductions can all be solved by means of the Painleve II equation but with different independent arguments. Some types of nontravelling singular solitary waves exist for the Dym equation there are two types of nonsingular nontravelling solitary wave solutions for some suitable potentials.
学科主题	Physics
URL标识	查看原文
公开日期	2012-08-29
内容类型	期刊论文
源URL	[http://ir.itp.ac.cn/handle/311006/12562]
专题	理论物理研究所_理论物理所1978-2010年知识产出
通讯作者	Lou, SY , NINGBO NORMAL COLL,INST MODERN PHYS,NINGBO 315211,PEOPLES R CHINA.
推荐引用方式 GB/T 7714	Lou, SY,Lou, SY , NINGBO NORMAL COLL,INST MODERN PHYS,NINGBO 315211,PEOPLES R CHINA.. Symmetries and similarity reductions of the dym equation[J]. PHYSICA SCRIPTA,1996,54(5):428-435.
APA	Lou, SY,&Lou, SY , NINGBO NORMAL COLL,INST MODERN PHYS,NINGBO 315211,PEOPLES R CHINA..(1996).Symmetries and similarity reductions of the dym equation.PHYSICA SCRIPTA,54(5),428-435.
MLA	Lou, SY,et al."Symmetries and similarity reductions of the dym equation".PHYSICA SCRIPTA 54.5(1996):428-435.