Darboux-covariant differential-difference operators and dressing chains
摘要
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.
引用
@article{arxiv.math-ph/0504003,
title = {Darboux-covariant differential-difference operators and dressing chains},
author = {Sergey Leble},
journal= {arXiv preprint arXiv:math-ph/0504003},
year = {2016}
}
备注
19 pages