Rotational quotient procedure: A tracking control continuation method for PDEs on radially symmetric domains

Continuation methods are capable of finding multiform solutions by tracking solution curves. However, these methods may fail to track some desired solution curves due to the interference of the rotational equivalent solutions on a radially symmetric domain. We propose a rotational quotient procedure that applies extra constraints to standard continuation which overcomes this difficulty. We solve a time-independent nonlinear Schrödinger equation on a disk domain to demonstrate the functionality of the proposed method.