Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2001-12-20
J. Phys. A: Math. & Gen., 35 (2002) 6963-6972
Nonlinear Sciences
Exactly Solvable and Integrable Systems
12 pages, infinitesimal symmetries and conservation laws are added
Scientific paper
10.1088/0305-4470/35/32/315
The technique of Darboux transformation is applied to nonlocal partner of two-dimensional periodic A_{n-1} Toda lattice. This system is shown to admit a representation as the compatibility conditions of direct and dual overdetermined linear systems with quantized spectral parameter. The generalization of the Darboux transformation technique on linear equations of such a kind is given. The connections between the solutions of overdetermined linear systems and their expansions in series at singular points neighborhood are presented. The solutions of the nonlocal Toda lattice and infinite hierarchies of the infinitesimal symmetries and conservation laws are obtained.
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