3 problems

Energetic stability threshold conjecture. There is $\omega_* \in (\omega_L,1)$ and $\Omega_* \in (0,1)$ such that the even wave satisfying (even-wave) is energetically stable for…

Let $b<0$, and consider the minimization problem in $A_{T/2}$ with fixed mass $m$, denoted by … operatorname{sn}{alpha,beta,k}(x)=frac{1}{alpha}operatorname{sn}left(frac{x}{beta},k…

Let $\psi_0 \in H^{\alpha}_{\rm per}(\mathbb{T})$ be the solution to the boundary-value problem with $c=c_0$ obtained from the main existence theorem, and let $X_0$ and…