11 problems

Degenerate-lump conjecture. An $M$th-order lump solution produced by the generalized long-wave limit method contains exactly $\frac{M(M+1)}{2}$ degenerate lump waves.

Let $\tau$ be a polynomial defining a KP lump solution of the form … with $k\in\mathbb{N}$ and $\deg\tau=k(k+1)$. A symmetric solution is one invariant under the reflections…

Nondegeneracy conjecture. For every $k\in\mathbb{N}$, the only smooth, evanescent solutions of this linearised equation are linear combinations of $\partial_xu_k^\star$ and…

Let $u_k^\star(x,y)=-2\partial_x^2\log \tau_k^\star(x,y)$ be the explicit symmetric lump solutions of the normalised KP equation … where $k\in\mathbb{N}$ and $\tau_k^\star$ is a po…

Consider the perturbed initial-value problem for the KP equation with the types of initial data studied by Kao, including $V$-type initial-value waves. Let $u(x,y,t)$ denote its so…

For a solution in the range of the Bäcklund transform, the codimension-one condition is intrinsic. Intrinsic codimension-one condition conjecture. This condition should correspond…

Multi-lump construction conjecture. The constructions from rational curves with cuspidal singularities should generalize to give similar real regular $M$-lump solutions for all…

Explicit-formula nonexistence conjecture. In this case, no explicit formula should be available for the homogeneous version of system $\left(\right)$.

Uniqueness conjecture. For $p=2$, there should be a unique ground state up to translation, and this ground state should be the lump solution $Q$.

Let critical points be classified as visible or non-visible, and let Propositions and be as in the source. Exhaustion conjecture. The reference to Proposition can be dropped, provi…

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