Manuel Mañas et al 2009 Inverse Problems 25 065007 doi:10.1088/0266-5611/25/6/065007
The multicomponent 2D Toda hierarchy: discrete flows and string equations
Manuel Mañas, Luis Martínez Alonso and Carlos Álvarez-Fernández
Show affiliationsThe multicomponent 2D Toda hierarchy is analyzed through a factorization problem associated with an infinite-dimensional group. A new set of discrete flows is considered and the corresponding Lax and Zakharov–Shabat equations are characterized. Reductions of block Toeplitz and Hankel bi-infinite matrix types are proposed and studied. Orlov–Schulman operators, string equations and additional symmetries (discrete and continuous) are considered. The continuous-discrete Lax equations are shown to be equivalent to a factorization problem as well as to a set of string equations. A congruence method to derive site-independent equations is presented and used to derive equations in the discrete multicomponent KP sector (and also for its modification) of the theory as well as dispersive Whitham equations.
- PACS
- MSC
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22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)
- Subjects
- Dates
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Issue 6 (June 2009)
Received 16 September 2008, in final form 3 March 2009
Published 21 April 2009
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The multicomponent 2D Toda hierarchy: discrete flows and string equations
Manuel Mañas et al 2009 Inverse Problems 25 065007
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