4 problems

Non-scattering-data dispersion-manageability conjecture. Given such $u_0$, both of the following assertions hold: (i) for fixed $t_0,t_1$, there exist $\gamma_+=\gamma_+(u_0)$ and…

Dispersion-manageability conjecture. There exists a Schwartz function $u_0$ such that, with $u(0,x)=u_0(x)$, either $(NLS)_\gamma$ or $(NLS)^\gamma$ is dispersion-manageable.

Delayed-blowup conjecture. The corresponding solution of either managed model does not blow up in $[0,T]$; thus, blowup can be delayed by dispersion or nonlinearity management.

Let $d$ be the spatial dimension and consider the nonlinear Schrödinger equation … with $21\sigma\in\mathbb{R}^+$, $21\lambda\in\mathbb{R}$, and $X$ a deterministic continuous func…