NDLI: Algebro-Geometric Solutions of the TD Hierarchy

Content Provider	Springer Nature Link
Author	Xue, Bo Zeng, Xin Geng, Xianguo
Copyright Year	2013
Abstract	Resorting to the Lenard recursion scheme, we derive the TD hierarchy associated with a 2 × 2 matrix spectral problem and establish Dubrovin-type equation in terms of the introduced elliptic variables. Based on the theory of algebraic curve, all the flows associated with the TD hierarchy are straightened under the Abel-Jacobi coordinates. An algebraic function ϕ, also called the meromorphic function, carrying the data of the divisor is introduced on the underlying hyperelliptic curve $\mathcal {K}_{n}$ . The known zeros and poles of ϕ allow to find theta function representations for ϕ by referring to Riemann’s vanishing theorem, from which we obtain algebro-geometric solutions for the entire TD hierarchy with the help of asymptotic expansion of ϕ and its theta function representation.
Ending Page	251
Page Count	23
Starting Page	229
File Format	PDF
ISSN	13850172
e-ISSN	15729656
Journal	Mathematical Physics, Analysis and Geometry
Issue Number	3
Volume Number	16
Language	English
Publisher	Springer Netherlands
Publisher Date	2013-05-24
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Geometry Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.) Theoretical, Mathematical and Computational Physics Analysis Relationships with integrable systems Group Theory and Generalizations Algebro-geometric solutions Series solutions Applications of Mathematics TD hierarchy
Content Type	Text
Resource Type	Article
Subject	Mathematical Physics Geometry and Topology

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