Orbital stability
In mathematical physics and the theory of partial differential equations, the solitary wave solution of the form u ( x , t ) = e − i ω t ϕ ( x ) {\displaystyle u(x,t)=e^{-i\omega t}\phi (x)} is said to be orbitally stable if any solution with the initial data sufficiently close to ϕ ( x ) {\displaystyle \phi (x)} forever remains in a given small neighborhood of the trajectory of e − i ω t ϕ ( x ) . {\displaystyle e^{-i\omega t}\phi (x).} == Formal definition == Formal definition is as follows.