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.
Categories: nlin.PS