10 problems

Kadomtsev–Petviashvili stability conjecture. $Q(x-t)$ is stable under the KP-II flow and unstable under the KP-I flow.

Stem-structure conjecture. Quasi-resonant collisions in the KPI equation may also generate stem structures analogous to those observed in quasi-resonant two-soliton solutions of th…

The Korteweg–de Vries equation is … Its one-soliton solutions are … The Kadomtsev–Petviashvili equations are … where the minus sign gives KPI and the plus sign gives KPII. Kadomtse…

Consider the fractional Kadomtsev–Petviashvili I (fKP-I) equation with fractional exponent $\alpha=1.5$, and let $c$ denote the speed of a traveling wave. A speed $c^*_{1.5}$ is ca…

The conjecture. Theorem should remain valid when the initial data are assumed to belong only to $E^1(\mathbb R^2)$.

Let $\epsilon$ be the small dispersion parameter, and let $a$, $b$, and $c_0$ be constants. Let $(x_0,y_0)$ be the position where a singularity of the Whitham system is expected to…

Consider the generalized KP equation … with $\epsilon$-independent initial data $u(x,y,0;\epsilon)=u_0(x,y)$, and assume its solution is at least $C^4$ for $t>0$. Let…

Let $u(x,y,t;\epsilon)$ solve the generalized KP equation with the same initial data as the solution $u(x,y,t)$ of the generalized dispersionless KP equation, and let $t_c$ denote…

Pearcey asymptotics conjecture. Near the first singularity, the solution has the asymptotic expansion

Ground-state uniqueness conjecture. The ground state solution is unique, up to the invariances of the problem.