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

2009/09/25 by Taras I. Lakoba, Lakoba, T. I.
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Nonlinear Photonic Systems #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.0909.4752

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.

Citations

• Universally‐Convergent Squared‐Operator Iteration Methods for Solitary Waves in General Nonlinear Wave Equations

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