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Algebro-geometric solutions of the Camassa-Holm hierarchy.

Fritz Gesztesy, Helge Holden (2003)

Revista Matemática Iberoamericana

We provide a detailed treatment of the Camassa-Holm (CH) hierarchy with special emphasis on its algebro-geometric solutions. In analogy to other completely integrable hierarchies of soliton equations such as the KdV or AKNS hierarchies, the CH hierarchy is recursively constructed by means of a basic polynomial formalism invoking a spectral parameter. Moreover, we study Dubrovin-type equations for auxiliary divisors and associated trace formulas, consider the corresponding algebro-geometric initial...

An integrable flow on a family of Hilbert Grassmannians.

Gomez, Rodrigo P. (1996)

The New York Journal of Mathematics [electronic only]

Andrew Lenard: a mystery unraveled.

Praught, Jeffery, Smirnov, Roman G. (2005)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Asymptotics of the partition function of a random matrix model

Pavel M. Bleher, Alexander Its (2005)

Annales de l’institut Fourier

We prove a number of results concerning the large $N$ asymptotics of the free energy of a random matrix model with a polynomial potential. Our approach is based on a deformation of potential and on the use of the underlying integrable structures of the matrix model. The main results include the existence of a full asymptotic expansion in even powers of $N$ of the recurrence coefficients of the related orthogonal polynomials for a one-cut regular potential and the double scaling asymptotics of the free...

Auxiliary linear problem, difference Fay identities and dispersionless limit of Pfaff-Toda hierarchy.

Takasaki, Kanehisa (2009)