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

We obtain linearized (i.e., non-global) convergence conditions for iterative methods that seek solitary waves with prescribed values of quadratic conserved quantities of multicomponent Hamiltonian nonlinear wave equations. These conditions extend the ones found for single-component solitary waves in a recent publication by J. Yang and the present author. We also show that, and why, these convergence conditions coincide with dynamical stability conditions for ground-state solitary waves. Notably, our analysis applies regardless of whether the number of quadratic conserved quantities, s, equals or is less than the number of equations, S. To illustrate the situation when s < S, we use one of our iterative methods to find ground-state solitary waves in spin-1 Bose–Einstein condensates in a magnetic field (s = 2, S = 3).