Inégalités a priori pour des tores lagrangiens invariants par des difféomorphismes symplectiques
Infinitesimal Brunovský form for nonlinear systems with applications to Dynamic Linearization
We define, in an infinite-dimensional differential geometric framework, the 'infinitesimal Brunovský form' which we previously introduced in another framework and link it with equivalence via diffeomorphism to a linear system, which is the same as linearizability by 'endogenous dynamic feedback'.
Initial boundary value problem for the mKdV equation on a finite interval
We analyse an initial-boundary value problem for the mKdV equation on a finite interval by expressing the solution in terms of the solution of an associated matrix Riemann-Hilbert problem in the complex -plane. This RH problem is determined by certain spectral functions which are defined in terms of the initial-boundary values at and . We show that the spectral functions satisfy an algebraic “global relation” which express the implicit relation between all boundary values in terms of spectral...
Integrability and beyond
Integrability and diffeomorphisms on target space.
Integrability of Hamiltonian systems and Birkhoff normal forms in the simple resonance case.
Integrable analytic vector fields with a nilpotent linear part
We study the normalization of analytic vector fields with a nilpotent linear part. We prove that such an analytic vector field can be transformed into a certain form by convergent transformations when it has a non-singular formal integral. We then prove that there are smoothly linearizable parabolic analytic transformations which cannot be embedded into the flows of any analytic vector fields with a nilpotent linear part.
Integrable anisotropic evolution equations on a sphere.
Integrable discrete equations derived by similarity reduction of the extended discrete KP hierarchy.
Integrable dynamical systems obtained by duplication
Integrable equations and their evolutions based on intrinsic geometry of Riemann spaces.
Integrable systems and projective images of Kummer surfaces
Integrable three-dimensional coupled nonlinear dynamical systems related to centrally extended operator Lie algebras and their Lax type three-linearization
The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the Lie algebra of integro-differential operators with matrix coefficients, extended by evolutions for eigenfunctions and adjoint eigenfunctions of the corresponding spectral problems, is obtained via some special Bäcklund transformation. The connection of this hierarchy with integrable by Lax two-dimensional Davey-Stewartson type systems is studied.
Integration of the EPDiff equation by particle methods
The purpose of this paper is to apply particle methods to the numerical solution of the EPDiff equation. The weak solutions of EPDiff are contact discontinuities that carry momentum so that wavefront interactions represent collisions in which momentum is exchanged. This behavior allows for the description of many rich physical applications, but also introduces difficult numerical challenges. We present a particle method for the EPDiff equation that is well-suited for this class of solutions and...
Integration of the EPDiff equation by particle methods∗∗∗∗∗∗
The purpose of this paper is to apply particle methods to the numerical solution of the EPDiff equation. The weak solutions of EPDiff are contact discontinuities that carry momentum so that wavefront interactions represent collisions in which momentum is exchanged. This behavior allows for the description of many rich physical applications, but also introduces difficult numerical challenges. We present a particle method for the EPDiff equation that...
Integration of the perturbated Jacobi problem.
Intertwining symmetry algebras of quantum superintegrable systems.
Invariance of the Gibbs measure for the Benjamin–Ono equation
In this paper we consider the periodic Benjemin-Ono equation.We establish the invariance of the Gibbs measure associated to this equation, thus answering a question raised in Tzvetkov [28]. As an intermediate step, we also obtain a local well-posedness result in Besov-type spaces rougher than , extending the well-posedness result of Molinet [20].
Invariant differential operators and Frobenius decomposition of a -variety. (Invariante Differentialoperatoren und die Frobenius-Zerlegung einer -Varietät.)
Invariant manifold of hyperbolic-elliptic type for nonlinear wave equation.