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

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

2009-09-25

arxiv.org/abs/0909.4752v1

Nonlinear Sciences

Pattern Formation and Solitons

20 pages, 1 multi-part figure

Scientific paper

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.

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