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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
Source PublicationPHYSICA SCRIPTA
KeywordPartial-differential Equations Dym Korteweg-devries Hierarchy Harry Linear Evolution-equations Sawada-kotera Equation Recursion Operator Painleve Property Discrete Eigenfunctions Singularity Analysis Kdv Equation
AbstractThe 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.
1996
ISSN0281-1847
Volume54Issue:5Pages:428-435
Subject AreaPhysics
Indexed BySCI
Document Type期刊论文
Identifierhttp://ir.itp.ac.cn/handle/311006/12562
Collection理论物理所科研产出_SCI论文
Corresponding AuthorLou, SY , NINGBO NORMAL COLL,INST MODERN PHYS,NINGBO 315211,PEOPLES R CHINA.
Recommended Citation
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.
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