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Discrete integrable systems, positivity, and continued fraction rearrangements
cluster algebras Laurent phenomenon positivity integrable systems
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2010/12/3
In this review article, we present a unified approach to solving discrete,integrable, possibly non-commutative, dynamical systems, including the Qand T-systems based on Ar.
Bäcklund Transformations as exact integrable time-discretizations for the trigonometric Gaudin model
Bä cklund Transformations trigonometric Gaudin model integrable time-discretizations
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2010/4/2
We construct a two-parameter family of B\"acklund transformations for the trigonometric classical Gaudin magnet. The approach follows closely the one introduced by E.Sklyanin and V.Kuznetsov (1998,199...
Integrable discretizations for the short wave model of the Camassa-Holm equation
Integrable discretizations short wave Camassa-Holm equation
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2010/4/2
The link between the short wave model of the Camassa-Holm equation (SCHE) and bilinear equations of the two-dimensional Toda lattice (2DTL) is clarified. The parametric form of N-cuspon solution of th...
Integrable discretizations of the short pulse equation
Integrable discretizations short pulse equation
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2010/4/6
In the present paper, we propose integrable semi-discrete and full-discrete analogues of the short pulse (SP) equation. The key of the construction is the bilinear forms and determinant structure of s...