An integrable flow on a family of Hilbert Grassmannians.
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.
Bäcklund transformations for first and second Painlevé hierarchies.
Bäcklund transformations for several cases of a type of generalized KdV equation.
Bäcklund-Darboux transformation for non-isospectral canonical system and Riemann-Hilbert problem.
Backlund-Darboux Transformations in Sato's Grassmannian
We define Bäcklund–Darboux transformations in Sato’s Grassmannian. They can be regarded as Darboux transformations on maximal algebras of commuting ordinary differential operators. We describe the action of these transformations on related objects: wave functions, tau-functions and spectral algebras.
Bethe ansatz, inverse scattering transform and tropical Riemann theta function in a periodic soliton cellular automaton for .
Bidifferential calculus approach to AKNS hierarchies and their solutions.
Bifurcation analysis for a delayed predator-prey system with stage structure.
Bifurcation of free vibrations for completely resonant wave equations
We prove existence of small amplitude, 2p/v-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency belonging to a Cantor-like set of positive measure and for a generic set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem.
Bi-integrable and tri-integrable couplings of a soliton hierarchy associated withSO(4)
In our paper, the theory of bi-integrable and tri-integrable couplings is generalized to the discrete case. First, based on the six-dimensional real special orthogonal Lie algebra SO(4), we construct bi-integrable and tri-integrable couplings associated with SO(4) for a hierarchy from the enlarged matrix spectral problems and the enlarged zero curvature equations. Moreover, Hamiltonian structures of the obtained bi-integrable and tri-integrable couplings are constructed by the variational identities....
Bound states in completely integrable systems with two types of particles
Boundary Liouville theory: Hamiltonian description and quantization.
By Magri's theorem, self-dual gravity is completely integrable.
-integrability test for discrete equations via multiple scale expansions.