Convergence conditions for iterative methods seeking multi-component solitary waves with prescribed quadratic conserved quantities

We obtain local (i.e., linearized) convergence conditions for iterative methods that seek solitary waves with prescribed values of quadratic conserved quantities of multi-component Hamiltonian nonlinear wave equations. These conditions extend the ones found for single-component solitary waves in [J. Yang and T.I. Lakoba, Stud. Appl. Math. {\bf 120}, 265–292 (2008)]. We also show that, and why, these convergence conditions coincide with dynamical stability conditions for ground-state solitary waves.