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

TL;DR

This paper derives local convergence conditions for iterative methods targeting multi-component solitary waves with specific conserved quantities, revealing their connection to the waves' dynamical stability.

Contribution

It extends previous convergence criteria from single-component to multi-component solitary waves and explains their equivalence to stability conditions.

Findings

Convergence conditions match stability criteria for ground-state solitary waves.

Conditions are derived for multi-component Hamiltonian nonlinear wave equations.

The work generalizes earlier results for single-component cases.

Abstract

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.