On the Virasoro structure of symmetry algebras of nonlinear partial differential equations.
Proof of the Treves theorem on the KdV hierarchy
A new, shorter, proof of the Treves theorem on an algebraic criterion for the first integrals of the KdV hierarchy is given, along with an addition to the theorem.
Soluzioni periodiche di PDEs Hamiltoniane
Presentiamo nuovi risultati di esistenza e molteplicità di soluzioni periodiche di piccola ampiezza per equazioni alle derivate parziali Hamiltoniane. Otteniamo soluzioni periodiche di equazioni «completamente risonanti» aventi nonlinearità generali grazie ad una riduzione di tipo Lyapunov-Schmidt variazionale ed usando argomenti di min-max. Per equazioni «non risonanti» dimostriamo l'esistenza di soluzioni periodiche di tipo Birkhoff-Lewis, mediante un'opportuna forma normale di Birkhoff e realizzando...
Stability investigation of quadratic systems with delay.
Stability of periodic waves in Hamiltonian PDEs
Partial differential equations endowed with a Hamiltonian structure, like the Korteweg–de Vries equation and many other more or less classical models, are known to admit rich families of periodic travelling waves. The stability theory for these waves is still in its infancy though. The issue has been tackled by various means. Of course, it is always possible to address stability from the spectral point of view. However, the link with nonlinear stability - in fact, orbital stability, since we are...
Supersymmetric representations and integrable fermionic extensions of the Burgers and Boussinesq equations.
Sur le caractère bien posé des équations de Schrödinger non linéaires
Symmetry group analysis and invariant solutions of hydrodynamic-type systems.
Symmetry properties of a generalized Korteweg-de Vries equation and some explicit solutions.
The Cauchy problem for the Gross–Pitaevskii equation
The equivalence between the Hamiltonian and Lagrangian formulations for the parametrization-invariant theories.
The Kowalevski's top and the method of Syzygies
A new algorithm for finding separation coordinates is tested on the example of Kowalev ski’s top.
Weakly nonlocal Hamiltonian structures: Lie derivative and compatibility.
WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity
Об эквивалентности двух семейств квантовых интегрируемых систем