Derrick's theorem
Derrick's theorem is an argument by physicist G. H. Derrick which shows that stationary localized solutions to a nonlinear wave equation or nonlinear Klein–Gordon equation in spatial dimensions three and higher are unstable. == Original argument == Derrick's paper, which was considered an obstacle to interpreting soliton-like solutions as particles, contained the following physical argument about non-existence of stable localized stationary solutions to the nonlinear wave equation ∇ 2 θ − ∂ 2 θ ∂ t 2 = 1 2 f ′ ( θ ) , θ ( x , t ) ∈ R , x ∈ R 3 , {\displaystyle \nabla ^{2}\theta -{\frac {\partial ^{2}\theta }{\partial t^{2}}}={\frac {1}{2}}f'(\theta ),\qquad \theta (x,t)\in \mathbb {R} ,\quad x\in \mathbb {R} ^{3},} now known under the name of Derrick's Theorem.