Using construction of logarithm of a difference operator, we present the Lax pair formalism for certain extension of the continuous version of the classical Toda lattice hierarchy, provide a well defined notion of tau function for its solutions, and give an explicit formulation of the relationship between the CP1 topological sigma model and the extended Toda hierarchy. We also establish an equivalence of the latter with certain extension of the nonlinear Schrodinger hierarchy.
The extended Toda hierarchy / Carlet, G.; Dubrovin, Boris; Zhang, Y. J.. - In: MOSCOW MATHEMATICAL JOURNAL. - ISSN 1609-3321. - 4:2(2004), pp. 313-332.
The extended Toda hierarchy
Dubrovin, Boris;
2004-01-01
Abstract
Using construction of logarithm of a difference operator, we present the Lax pair formalism for certain extension of the continuous version of the classical Toda lattice hierarchy, provide a well defined notion of tau function for its solutions, and give an explicit formulation of the relationship between the CP1 topological sigma model and the extended Toda hierarchy. We also establish an equivalence of the latter with certain extension of the nonlinear Schrodinger hierarchy.| File | Dimensione | Formato | |
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