Perturbation theory for nonlinear Schrödinger equations

Treating the nonlinear term of the Gross–Pitaevskii nonlinear Schrödinger equation as a perturbation of an isolated discrete eigenvalue of the linear problem one obtains a Rayleigh–Schrödinger power series. This power series is proved to be convergent when the parameter representing the intensity of the nonlinear term is less in absolute value than a threshold value, and it gives a stationary solution to the nonlinear Schrödinger equation.