7 problems

Consider the $L^2$-supercritical generalized Korteweg–de Vries equation in the odd-power case, and the convergence around spatial zero asserted in Theorems … . Odd-power convergenc…

Let $k\geq 3$ and consider the $k$-generalized Korteweg-de Vries equation on the periodic domain, with initial data in the Sobolev space $H^s(\mathbb T)$. Unconditional well-posedn…

For a solution $u$ of the generalized KdV equation, let $Q_c$ denote a rescaled soliton profile, let $a_j$ be shifts, and let $r(x,t)$ denote radiation. The soliton speeds are…

Let $\nu$ denote the blow-up rate for the critical generalized Korteweg–de Vries equation. Blow-up-rate conjecture. All blow-up rates are possible in the range … The paper construc…

Backward-time separation conjecture. The behavior as $t\to-\infty$ is not the same as for $t\to+\infty$; specifically, the relative distance is of order $|t|$.

Universal dispersive-profile conjecture. There exists a universal $v_0$, minimizing a certain functional related to energy quantities, for example

For the quartic generalized Korteweg–de Vries equation, consider a general solution satisfying suitable assumptions. A decomposition into decoupled solitary waves and a dispersive…