7 problems

Scattering conjecture for critical gKdV. There exist functions

Below-ground-state almost-periodic-solution conjecture. There does not exist a nonzero almost periodic solution $u$ to $(1.1)$ satisfying

Let $u$ solve the focusing, mass-critical generalized KdV equation $(1.1)$ with initial data $u(0,x)=u_0\in L^2(\mathbb{R})$, and let … be the ground state, which satisfies…

Let $u_0\in L_2(\mathbb R)$ be smooth initial data with a single maximum, let $\epsilon\ll1$ be the dispersion parameter, and let $t_c$ be the break-up time of the corresponding ge…

Let $P$ be the solution of the ODE defining the proposed blow-up profile, and let $u(x,t)$ solve the generalized Korteweg–de Vries equation for $n=5$ with smooth initial data…

Let $Q$ be the soliton of the quartic generalized Korteweg–de Vries equation, and let $u(x,t)$ solve that equation for $n=4$ with smooth initial data $u_0\in L_2(\mathbb{R})$ of su…

Let $u$ solve the mass-critical generalized KdV equation on ${\mathbb R}\times{\mathbb R}$, let $u_0\in L^2_x({\mathbb R})$ be its initial data, let $M(u_0)$ denote its mass, and l…