Trace Formulae for the Nonlinearization of Periodic Finite-Bands Dirac Spectral Problem
Received:April 09, 2015  Revised:September 14, 2015
Key Words: trace formulae   periodic $N$-bands Dirac operator   nonlinearization   integrable Hamiltonian system  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.61473332), the Natural Science Foundation of Zhejiang Province (Grant No.LQ14A010009) and the Natural Science Foundation of Huzhou City (Grant No.2013YZ06).
Author NameAffiliation
Guangyao ZHANG School of Science, Huzhou University, Zhejiang 313000, P. R. China 
Huiqian ZHU School of Science, Huzhou University, Zhejiang 313000, P. R. China 
Hits: 2600
Download times: 2144
Abstract:
      This paper deals with a Dirac operator with periodic and finite-bands potentials. Taking advantage of the commutativity of the monodromy operator and the Dirac operator, we define the Bloch functions and multiplicator curve, which leads to the formula of Dubrovin-Novikov's type. Further, by calculation of residues on the complex sphere and via gauge transformation, we get the trace formulae of eigenfunctions corresponding to the left end-points and right end-points of the spectral bands, respectively. As an application, we obtain a completely integrable Hamiltonian system in Liouville sense through nonlinearization of the Dirac spectral problem.
Citation:
DOI:10.3770/j.issn:2095-2651.2016.02.007
View Full Text  View/Add Comment