Untitled

Self Cite

Section: Discussionmentioning

confidence: 99%

Dressing chain for the acoustic spectral problem

Адлер

Shabat

2006

Self Cite

“…corresponds to the Lagrangian Degenerate Lagrangians linear inq n play an important role in the theory of Bäcklund transformations [4]. The Lagrangian form of the dressing chain…”

Section: Dressing Chainmentioning

confidence: 99%

The structure of polynomial conservation laws

Garifullin

Shabat

2009

Self Cite

“…A periodic closure of the chain produces integrable bi-Hamiltonian finite-dimensional systems and finite-gap potentials in some special cases [25]. The Boussinesq case was explored in [22] (also see [26]). The chain equations for the classical differential ZS problem and two types of the DT were introduced in [27] (also see [15]).…”

Section: The One-field First-order Shift Operator Evolutionmentioning

confidence: 99%

Necessary Covariance Conditions for a One-Field Lax Pair

Leble

2005

We study the covariance with respect to Darboux transformations of polynomial differential and difference operators with coefficients given by functions of one basic field. In the scalar (Abelian) case, the functional dependence is established by equating the Frechèt differential (the first term of the Taylor series on the prolonged space) to the Darboux transform; a Lax pair for the Boussinesq equation is considered. For a pair of generalized Zakharov-Shabat problems (with differential and shift operators) with operator coefficients, we construct a set of integrable nonlinear equations together with explicit dressing formulas. Non-Abelian special functions are fixed as the fields of the covariant pairs. We introduce a difference Lax pair, a combined gauge-Darboux transformation, and solutions of the Nahm equations.