Boundedness of the local energy truncation
K_L>0 and λ_T≥2g_LT²/K_L bound this local energy below. At fixed transverse intensity η_eq=−g_LT|Ω_T|²/K_L, giving expansion for g_LT>0. This is not a complete stable localized particle solution.
Based on the final manuscript · Chapter 3
K_L>0 and λ_T≥2g_LT²/K_L bound this local energy below. At fixed transverse intensity η_eq=−g_LT|Ω_T|²/K_L, giving expansion for g_LT>0. This is not a complete stable localized particle solution.
Chapter reference: Final collected manuscript · Chapter 3, equations (3.77) · ASD-BOOK-ddbade997b45
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Final collected manuscript · Chapter 3, equations (3.77)
K_L>0 and λ_T≥2g_LT²/K_L bound this local energy below. At fixed transverse intensity η_eq=−g_LT|Ω_T|²/K_L, giving expansion for g_LT>0. This is not a complete stable localized particle solution.
Conditions retained in this adoption
- Vanishing boundary variations; constant g_LT, K_L and λ_T.
- K_L>0 and λ_T≥2g_LT²/K_L
- Minimize over η at fixed transverse intensity.
Specific unresolved source issues
- Full gradient energy, microscopic parameters, long-range sources and stable configurations remain research tasks.
Source locators: p1240 · p1241 · p1243 · p1244 · p1245 · p1246 · p1249 · p1250 · p1251 · p1252 · p1284 · 最终合订稿 · 第三章式 (3.77)
Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e
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EM-f06476f55cae · 第三章 / Chapter 3 · (3.77), PDF p. 18
Dependencies
algebraCandidate nonlinear longitudinal–transverse couplingASD-WEB-EM-041