HIERARCHIES OF NONLINEAR INTEGRABLE q-DIFFERENCE EQUATIONS FROM SERIES OF LAX PAIRS
نویسنده
چکیده
We present, for the first time, two hierarchies of nonlinear, integrable q-difference equations, one of which includes a q-difference form of each of the second and fifth Painlevé equations, qPII and qPV, the other includes qPIII. All the equations have multiple free parameters. A method to calculate a 2× 2 Lax pair for each equation in the hierarchy is also given.
منابع مشابه
A Lax Operator Hierarchy for the New Fifth Order Integrable System
We consider the Lax representation of the new two-component coupled integrable system recently discovered by the author. Connection of the hierarchy of infinitely many Lax pairs with each other is presented.
متن کاملGauge Transformations and Reciprocal Links in 2 + 1
Generalized Lax equations are considered in the spirit of Sato theory. Three decompositions of an underlying algebra of pseudo-diierential operators lead, in turn, to three diierent classes of integrable nonlinear hierarchies. These are associated with Kadomtsev-Petviashvili, modiied Kadomtsev-Petviashvili and Dym hierarchies in 2+1 dimensions. Miura-and auto-BB acklund transformations are show...
متن کاملTwo integrable lattice hierarchies and their respective Darboux transformations
Two integrable lattice hierarchies associated with two discrete matrix spectral problems are derived, and the infinitely many conservation laws of the first integrable model is obtained. Moreover, the Darboux transformations based on different Darboux matrixes (2.3.4) and (3.2.4) for the above-mentioned integrable hierarchies are established with the help of two different gauge transformations ...
متن کاملSymbolic Computation of Lax Pairs of Partial Difference Equations using Consistency Around the Cube
A three-step method due to Nijhoff and Bobenko & Suris to derive a Lax pair for scalar partial difference equations (P Es) is reviewed. The method assumes that the P Es are defined on a quadrilateral, and consistent around the cube. Next, the method is extended to systems of P Es where one has to carefully account for equations defined on edges of the quadrilateral. Lax pairs are presented for ...
متن کاملIntegrable (2 + 1)-Dimensional Spin Models with Self-Consistent Potentials
Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimately connected to the nonlinear Schrödinger family of equations. In this paper, we identify three different integrable spin systems in (2 + 1) dimensions by introducing the interaction of the spin field with more than o...
متن کامل