-wave equations with orthogonal algebras: and reductions and soliton solutions.
Nambu-Poisson structures and their foliations.
New exact solutions for the -dimensional Broer-Kaup-Kupershmidt equations.
New exact traveling wave solutions for compound KdV-Burgers equations in mathematical physics.
New explicit and exact solutions for the Nizhnik-Novikov-Vesselov equation.
New solitons and periodic solutions for Thekadomtsev-Petviashvili equation.
Nilpotent and recursive flows.
Nonarchimedean dynamical systems
Nonclassical approximate symmetries of evolution equations with a small parameter.
Noncommutative root space Witt, Ricci flow, and Poisson bracket continual Lie algebras.
Nondegenerate systems and generic properties of the integrable Hamiltonian systems
Nonlinear oscillations of completely resonant wave equations
Nonlinear Schrödinger equation on four-dimensional compact manifolds
We prove two new results about the Cauchy problem in the energy space for nonlinear Schrödinger equations on four-dimensional compact manifolds. The first one concerns global well-posedness for Hartree-type nonlinearities and includes approximations of cubic NLS on the sphere as a particular case. The second one provides, in the case of zonal data on the sphere, local well-posedness for quadratic nonlinearities as well as a necessary and sufficient condition of global well-posedness for small energy...
Nonlinear vibrations of completely resonant wave equations
We present recent existence results of small amplitude periodic and quasi-periodic solutions of completely resonant nonlinear wave equations. Both infinite-dimensional bifurcation phenomena and small divisors difficulties occur. The proofs rely on bifurcation theory, Nash-Moser implicit function theorems, dynamical systems techniques and variational methods.
Notes on symplectic non-squeezing of the KdV flow
We prove two finite dimensional approximation results and a symplectic non-squeezing property for the Korteweg-de Vries (KdV) flow on the circle . The nonsqueezing result relies on the aforementioned approximations and the finite-dimensional nonsqueezing theorem of Gromov [14]. Unlike the work of Kuksin [22] which initiated the investigation of non-squeezing results for infinite dimensional Hamiltonian systems, the nonsqueezing argument here does not construct a capacity directly. In this way our...