Geodesic
Formal diagonalisation of Lax--Darboux schemes
Modelirovanie i analiz informacionnyh sistem, Tome 22 (2015) no. 6, pp. 795-817

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We discuss the concept of Lax–Darboux scheme and illustrate it on well known examples associated with the Nonlinear Schrödinger (NLS) equation. We explore the Darboux links of the NLS hierarchy with the hierarchy of Heisenberg model, principal chiral field model as well as with differential-difference integrable systems (including the Toda lattice and differential-difference Heisenberg chain) and integrable partial difference systems. We show that there exists a transformation which formally diagonalises all elements of the Lax–Darboux scheme simultaneously. It provides us with generating functions of local conservation laws for all integrable systems obtained. We discuss the relations between conservation laws for systems belonging to the Lax–Darboux scheme.
Keywords: Lax-Darboux schemes, nonlinear Schrödinger equation
Mots-clés : formal diagonalisation, NLS. 
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     author = {A. V. Mikhailov},
     title = {Formal diagonalisation of {Lax--Darboux} schemes},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {795--817},
     publisher = {mathdoc},
     volume = {22},
     number = {6},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2015_22_6_a5/}
}
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A. V. Mikhailov. Formal diagonalisation of Lax--Darboux schemes. Modelirovanie i analiz informacionnyh sistem, Tome 22 (2015) no. 6, pp. 795-817. http://geodesic.mathdoc.fr/item/MAIS_2015_22_6_a5/