mblasco137
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- TL;DR
- What hierarchy of mathematical and numerical evidence distinguishes a converged localized field configuration from a genuinely stable solution—particularly topology, virial conditions, spectral/linear stability, and nonlinear orbital stability?
In nonlinear classical field theories that admit localized or topological solutions (for example, Skyrme-type or Faddeev–Skyrme-type models), what mathematical and numerical evidence is normally considered sufficient to distinguish a genuinely stable localized solution from a stationary numerical configuration?
In particular, how should one distinguish the roles of topology, Derrick/virial conditions, spectral stability, linear stability, and nonlinear orbital stability?
Suppose a numerical calculation produces a converged finite-energy localized configuration, satisfies the relevant constraint and virial checks, and survives mesh and domain refinement. My understanding is that this establishes considerably less than nonlinear dynamical stability.
What would be an appropriate hierarchy of evidence from existence of a stationary solution through spectral/linear stability to nonlinear persistence or orbital stability?
Are there standard benchmark models, theorems, or references that illustrate what is required at each level?
In particular, how should one distinguish the roles of topology, Derrick/virial conditions, spectral stability, linear stability, and nonlinear orbital stability?
Suppose a numerical calculation produces a converged finite-energy localized configuration, satisfies the relevant constraint and virial checks, and survives mesh and domain refinement. My understanding is that this establishes considerably less than nonlinear dynamical stability.
What would be an appropriate hierarchy of evidence from existence of a stationary solution through spectral/linear stability to nonlinear persistence or orbital stability?
Are there standard benchmark models, theorems, or references that illustrate what is required at each level?