Symmetries of control systems
Symmetries of the control systems of the form , , are studied. Some general results concerning point symmetries are obtained. Examples are provided.
Symmetries of the nonlinear Schrödinger equation
Symmetries of the defocusing nonlinear Schrödinger equation are expressed in action-angle coordinates and characterized in terms of the periodic and Dirichlet spectrum of the associated Zakharov-Shabat system. Application: proof of the conjecture that the periodic spectrum of a Zakharov-Shabat operator is symmetric,i.e. for all , if and only if the sequence of gap lengths, , is symmetric with respect to .
Symmetry group analysis and invariant solutions of hydrodynamic-type systems.
Symmetry in Architecture
Symmetry operators for the Fokker-Planck-Kolmogorov equation with nonlocal quadratic nonlinearity.
Symmetry properties of a generalized Korteweg-de Vries equation and some explicit solutions.
Symplectic Capacities in Manifolds
Symplectic capacities coinciding on convex sets in the standard symplectic vector space are extended to any subsets of symplectic manifolds. It is shown that, using embeddings of non-smooth convex sets and a product formula, calculations of some capacities become very simple. Moreover, it is proved that there exist such capacities which are distinct and that there are star-shaped domains diffeomorphic to the ball but not symplectomorphic to any convex set.
Symplectic capacities in two dimensions.
Symplectic convexity theorems and coadjoint orbits
Symplectic difference systems: oscillation theory and hyperbolic Prüfer transformation.
Symplectic field theory approach to studying ergodic measures related with nonautonomous Hamiltonian systems.
Symplectic geometry on moduli spaces of stable pairs
Symplectic gluing along hypersurfaces and resolution of isolated orbifold singularities.
Symplectic homology II. A general construction.
Symplectic Homology via Generating Functions.
Symplectic integrators to stochastic Hamiltonian dynamical systems derived from composition methods.
Symplectic manifolds with contact type boundaries.
Symplectic models of groups with noncommutative spaces
Symplectic packings and algebraic geometry. (with an Appendix by Y. Karshon).
Symplectic phase flow approximation for the numerical integration of canonical systems.