2 problems

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Conjecture that nonlocal effects suppress transverse instability of dark solitons
Nonlocal transverse-stability conjecture. Nonlocal effects can suppress the transverse instability of dark solitons.
Conjectureopendark-solitons nonlocal-equations stabilityarXiv posted 2 days ago
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de Laire–Mennuni's minimization-curve conjecture for nonlocal dark solitons
Let $E_\textup{min}$ be the minimization curve and let $\mathfrak{q}_*$ be the threshold defined by the condition that every $v$ with energy at most $E_\textup{min}(\mathfrak{q})$ …
Conjectureopendark-solitons nonlinear-schrodinger-equations variational-methodsarXiv posted 2 days ago

Conjecture that nonlocal effects suppress transverse instability of dark solitons