A continuation method for positive bound states of m-coupled nonlinear Schrödinger equations

We develop a stable continuation method for the computation of positive bound states of time-independent, m-coupled nonlinear algebra equation (DNLS) which describe a m-coupled nonlinear Schrödinger equation. The solution curve with respect to some parameter of the DNLS is then followed by the proposed method. For a one-component DNLS, we develop a iterative method for computation of positive ground state solution. For a m-coupled DNLS, we prove that m radially symmetric positive bound states will bifurcate into m different positive bound states at a finite repulsive inter-component scattering length. Numerical results show that various positive bound states of a three-component DNLS are solved efficiently and reliably by the continuation method.