3 problems

Consider the dissipative modified Korteweg–de Vries equation on the real line … The scaling-critical index of the mKdV equation is $-\frac{1}{2}$, while that of the equation with o…

Let $(q,r)$ be a Schrödinger-admissible pair with $4<q<\finite$ and $gamma=1/q$. Let $A_{q,r}$ denote the sharp Airy–Strichartz constant, let $\widetilde A_{q,r}$ denote the Frank–…

For the modified Korteweg–de Vries equation, consider breathers, namely spatially localized, time-periodic solutions; a breather has positive velocity when its propagation velocity…