Orbital stability

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