Derrick's theorem

Derrick's theorem is a result in the field of mathematical physics, particularly in the study of field theories and solitons. It concerns the stability of soliton solutions to certain field equations, specifically addressing the stability under small perturbations of the solutions. The theorem states that if a field configuration (such as a soliton) is localized and satisfies certain energy conditions, then it is stable against small perturbations if and only if its energy does not decrease under rescaling of the spatial variables.