5 problems

KAM existence conjecture. There exist three explicit functions $a,b_d,b_a:\mathbb R^+\to\mathbb R^+$ such that

A posteriori KAM existence conjecture. There exist three explicit functions $a,b_d,b_a:\mathbb R^+\to\mathbb R^+$ such that

An equation is dispersive if all branches of its dispersion relation $\omega(k)$ are real valued for $k\in\mathbb{R}$. A system is Hamiltonian if it admits a Hamiltonian formulatio…

Let ${\mathcal V}$ be the algebra of differential functions specified for Case A2. The conserved densities $h_n$ of the Case A2 system can be chosen in ${\mathcal V}$ for all $n$.…

Let $v(x,t)$ be a smooth solution of the leading hyperbolic equation … is a Hamiltonian perturbation and let $u=u(x,t;\epsilon)$ denote a solution of it on the same domain in the…