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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.
1996
发表期刊PHYSICA SCRIPTA
ISSN0281-1847
卷号54期号:5页码:428-435
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.
部门归属FUDAN UNIV,DEPT PHYS,SHANGHAI 200433,PEOPLES R CHINA; ACAD SINICA,INST THEORET PHYS,BEIJING 100080,PEOPLES R CHINA
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
学科领域Physics
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收录类别SCI
文献类型期刊论文
条目标识符http://ir.itp.ac.cn/handle/311006/12562
专题理论物理所1978-2010年知识产出
通讯作者Lou, SY , NINGBO NORMAL COLL,INST MODERN PHYS,NINGBO 315211,PEOPLES R CHINA.
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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.
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