Bäcklund transformations for high-order constrained flows of the AKNS hierarchy: canonicity and spectrality property
نویسندگان
چکیده
New infinite number of oneand two-point Bäcklund transformations (BTs) with explicit expressions are constructed for the high-order constrained flows of the AKNS hierarchy. It is shown that these BTs are canonical transformations including Bäcklund parameter η and a spectrality property holds with respect to η and the ’conjugated’ variable μ for which the point (η, μ) belongs to the spectral curve. Also the formulas of m-times repeated Darboux transformations for the high-order constrained flows of the AKNS hierarchy are presented.
منابع مشابه
Canonical explicit Bäcklund transformations with spectrality for constrained flows of soliton hierarchies
It is shown that explicit Bäcklund transformations (BTs) for the high-order constrained flows of soliton hierarchy can be constructed via their Darboux transformations and Lax representation, and these BTs are canonical transformations including Bäcklund parameter η and possess a spectrality property with respect to η and the ’conjugated’ variable μ for which the pair (η, μ) lies on the spectra...
متن کاملBäcklund Transformation for the BC-Type Toda Lattice
We study an integrable case of n-particle Toda lattice: open chain with boundary terms containing 4 parameters. For this model we construct a Bäcklund transformation and prove its basic properties: canonicity, commutativity and spectrality. The Bäcklund transformation can be also viewed as a discretized time dynamics. Two Lax matrices are used: of order 2 and of order 2n + 2, which are mutually...
متن کاملBäcklund transformations for the constrained dispersionless hierarchies and dispersionless hierarchies with self-consistent sources
The Bäcklund transformations between the constrained dispersionless KP hierarchy (cdKPH) and the constrained dispersionless mKP hieararchy (cdmKPH) and between the dispersionless KP hieararchy with self-consistent sources (dKPHSCS) and the dispersionless mKP hieararchy with self-consistent sources (dmKPHSCS) are constructed. The auto-Bäcklund transformations for the cdmKPH and for the dmKPHSCS ...
متن کاملIntegrable Rosochatius deformations of higher-order constrained flows and the soliton hierarchy with self-consistent sources
Abstract We propose a systematic method to generalize the integrable Rosochatius deformations for finite dimensional integrable Hamiltonian systems to integrable Rosochatius deformations for infinite dimensional integrable equations. Infinite number of the integrable Rosochatius deformed higher-order constrained flows of some soliton hierarchies, which includes the generalized integrable Hénon-...
متن کامل2 On generating functions in the AKNS hierarchy
It is shown that the self-induced transparency equations can be interpreted as a generating function for as positive so negative flows in the AKNS hierarchy. Mutual commutativity of these flows leads to other hierarchies of integrable equations. In particular, it is shown that stimulated Raman scattering equations generate the hierarchy of flows which include the Heisenberg model equations. Thi...
متن کامل