Darboux-covariant differential-difference operators and dressing chains
Leble, Sergey
arXiv, 0504003 / Harvested from arXiv
Text on arXiv
The general approach to chain equations derivation for the function generated by a Miura transformation analog is developing to account evolution (second Lax equation) and illustrated for Sturm-Liouville differential and difference operators. Polynomial differential operators case is investigated. Covariant sets of potentials are introduced by a periodic chain closure. The symmetry of the system of equation with respect to permutations of the potentials is used for the direct construction of solutions of the chain equations. A "time" evolution associated with some Lax pair is incorporated in the approach via closed t-chains. Both chains are combined in equations of a hydrodynamic type. The approach is next developed to general Zakharov-Shabat differential and difference equations, the example of 2x2 matrix case and NS equation is traced.
Publié le : 2005-04-01
Classification:  Mathematical Physics,  58F07 
@article{0504003,
     author = {Leble, Sergey},
     title = {Darboux-covariant differential-difference operators and dressing chains},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0504003}
}

Leble, Sergey. Darboux-covariant differential-difference operators and dressing chains. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0504003/