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

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).