{"paper":{"title":"Instability of vortex solitons for 2D focusing NLS","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tetsu Mizumachi","submitted_at":"2006-05-01T06:19:45Z","abstract_excerpt":"We study instability of a vortex soliton $e^{i(m\\theta+\\omega t)}\\phi_{\\omega,m}(r)$ to $$iu_t+\\Delta u+|u|^{p-1}u=0,\\quad\\text{for $x\\in\\R^n$, $t>0$,}$$ where $n=2$, $m\\in\\N$ and $(r,\\theta)$ are polar coordinates in $\\R^2$. Grillakis \\cite{Gr} proved that every radially standing wave solutions are unstable if $p>1+4/n$. However, we do not have any examples of unstable standing wave solutions in the subcritical case $(p<1+n/4)$.\n  Suppose $\\phi_{\\omega,m}$ is nonnegative. We investigate a limiting profile of $\\phi_{\\omega,m}$ as $m\\to\\infty$ and prove that for every $p>1$, there exists an $m_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605032","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}