5 problems

Uniform-validity conjecture. The asymptotic formula $$ holds uniformly for $u$ in every compact subset of $(0,1)…

Lump-circle radius conjecture. For both cases, the radius satisfies

Let $\Theta_n^{\pm}(x,t)$ be the polynomials defined by … where $P_n(x,t)$ and $Q_n(x,t)$ are the polynomials in the generalised rational solution of the Boussinesq equation. Bilin…

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