5 problems

Let the 3D Zakharov–Kuznetsov equation be given by, and let the soliton solutions be those defined by --. A perturbation is understood to be of soliton-like initial data, and suffi…

For $\omega<\omega_c$, consider initial data of the form … Here $Q_\omega$ is a cubic-quintic ground state, $M$ denotes mass, and…

Let $E$ satisfy $|E|\ll 10$. A small-energy blow-up conjecture asserts that the KdV soliton for small $a$ is stable under NV dynamics, while the KdV soliton for large $a$ is unstab…

Let $E\ll -1$. A large-negative-energy behavior conjecture asserts that the KdV soliton is stable under NV dynamics and that localized initial data will be radiated away to infinit…

Let $E\gg 1$. A large-positive-energy behavior conjecture asserts that the KdV soliton for small $a$ is stable under NV dynamics, whereas the KdV soliton for large $a$ is unstable…