scholarly journals The Riemann theta function solutions for the hierarchy of Bogoyavlensky lattices

2018 ◽  
Vol 371 (2) ◽  
pp. 1483-1507 ◽  
Author(s):  
Jiao Wei ◽  
Xianguo Geng ◽  
Xin Zeng
Keyword(s):  
Theta Function ◽  
Riemann Theta Function

On a Toda lattice hierarchy: Lax pair, integrable symplectic map and algebraic–geometric solution

2018 ◽  
Vol 32 (28) ◽  
pp. 1850344
Author(s):  
Xiao Yang ◽  
Dianlou Du
Keyword(s):  
Spectral Problem ◽  
Theta Function ◽  
Toda Lattice ◽  
Burgers Equation ◽  
Lax Pair ◽  
Discrete Variable ◽  
Riemann Theta Function ◽  
Symplectic Map ◽  
Discrete Counterpart ◽  
Toda Lattice Hierarchy

A Toda lattice hierarchy is studied by introducing a new spectral problem which is a discrete counterpart of the generalized Kaup–Newell spectral problem. Based on the Lenard recursion equation, Lax pair of the hierarchy is given. Further, the discrete spectral problem is nonlinearized into an integrable symplectic map. As a result, an algebraic–geometric solution in Riemann theta function of the hierarchy is obtained. Besides, two equations, the Volterra lattice and a (2[Formula: see text]+[Formula: see text]1)-dimensional Burgers equation with a discrete variable, yielded from the hierarchy are also solved.

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