Solution of the finite complex Toda lattice by the method of inverse spectral problem

2013 ◽  
Vol 219 (10) ◽  
pp. 5550-5563
Author(s):  
Aydin Huseynov ◽  
Gusein Sh. Guseinov
Keyword(s):  
Spectral Problem ◽  
Toda Lattice ◽  
Inverse Spectral Problem ◽  
Finite Complex ◽  
Inverse Spectral

scholarly journals Exact solutions of the semi-infinite Toda lattice with applications to the inverse spectral problem

2004 ◽  
Vol 2004 (5) ◽  
pp. 435-451
Author(s):  
E. K. Ifantis ◽  
K. N. Vlachou
Keyword(s):  
Differential Equation ◽  
Probability Measure ◽  
Exact Solutions ◽  
Spectral Problem ◽  
Toda Lattice ◽  
Inverse Spectral Problem ◽  
Initial Conditions ◽  
Inverse Spectral Problems ◽  
Spectral Problems ◽  
Inverse Spectral

Several inverse spectral problems are solved by a method which is based on exact solutions of the semi-infinite Toda lattice. In fact, starting with a well-known and appropriate probability measureμ, the solutionαn(t),bn(t)of the Toda lattice is exactly determined and by takingt=0, the solutionαn(0),bn(0)of the inverse spectral problem is obtained. The solutions of the Toda lattice which are found in this way are finite for everyt>0and can also be obtained from the solutions of a simple differential equation. Many other exact solutions obtained from this differential equation show that there exist initial conditionsαn(0)>0andbn(0)∈ℝsuch that the semi-infinite Toda lattice is not integrable in the sense that the functionsαn(t)andbn(t)are not finite for everyt>0.

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