2024/12/30 by Joel Kübler, Kübler, Joel
Mathematics · #Advanced Mathematical Physics Problems
paper · pdf · doi:10.48550/arxiv.2501.00109
We consider rotating wave solutions of the nonlinear wave equation \ \beginaligned ∂t2 v - Δv + m v amp; = |v|p-2 v amp;amp; in ℝ × B
v amp; = 0 amp;amp; on ℝ × ∂ B \endaligned . for 21. We find that the structure of the spectrum of Lα strongly depends on the quantity σ= \fracπ√(α2- 1) - \arccos \frac1α gt; 0 . By giving precise estimates for certain sequences of Bessel function zeros, we can classify the spectrum for all α>1 such that σ is rational and further find that the existence of accumulation points explicitly depends on arithmetic properties of σ. Using these characterizations, we deduce existence and symmetry breaking results for ground state solutions of the reduced equation, extending known results.