Matrix analysis
SIAM Journal on Scientific Computing
Computing the Ground State Solution of Bose--Einstein Condensates by a Normalized Gradient Flow
SIAM Journal on Scientific Computing
A mode elimination technique to improve convergence of iteration methods for finding solitary waves
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Computing Ground States of Spin-1 Bose-Einstein Condensates by the Normalized Gradient Flow
SIAM Journal on Scientific Computing
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We obtain linearized (i.e., non-global) 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 a recent publication by 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