2 problems

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Asymptotic stability conjecture for the perturbed $phi^4$ kink
Consider the constant-coefficient $phi^4$ equation … with nonlinearity $F'(u)=u^3-u$ , and its kink solution. Asymptotic stability means that solutions starting near the kink in the…
Conjectureopenscalar-field-equations solitary-waves stability-analysisarXiv posted 2 days ago
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Hod–Piran asymptotic behaviour conjecture for weakly charged scalar fields
Let $(\phi,F)$ be a solution of the Maxwell-Charged-Scalar field system with no particular symmetry assumption on a Reissner--Nordström space-time. Define the Maxwell charge $Q$ by…
Conjectureopenasymptotic-decay black-hole-physics scalar-field-equationsarXiv posted 2 days ago

Asymptotic stability conjecture for the perturbed phi4phi^4phi4 kink