Analytical and numerical methods for the CMKdV-II equation.
Andrew Lenard: a mystery unraveled.
Asymptotics of the partition function of a random matrix model
We prove a number of results concerning the large 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 of the recurrence coefficients of the related orthogonal polynomials for a one-cut regular potential and the double scaling asymptotics of the free...
Attracting domains for semi-attractive transformations of Cp.
Let F be a germ of analytic transformation of (Cp, 0). We say that F is semi-attractive at the origin, if F'(0) has one eigenvalue equal to 1 and if the other ones are of modulus strictly less than 1. The main result is: either there exists a curve of fixed points, or F - Id has multiplicity k and there exists a domain of attraction with k - 1 petals. We also study the case where F is a global isomorphism of C2 and F - Id has multiplicity k at the origin. This work has been inspired by two papers:...
Auto-Bäcklund transformation and exact analytical solutions for the Kupershmidt equation.
Auxiliary linear problem, difference Fay identities and dispersionless limit of Pfaff-Toda hierarchy.