Computational aspects of the Maslov index of solitary waves - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2009

Computational aspects of the Maslov index of solitary waves

Résumé

When solitary waves are characterized as homoclinic orbits of a finite-dimensional Hamiltonian system, they have an integer-valued topological invariant, the Maslov index. We are interested in developing a robust numerical algorithm to compute the Maslov index, to understand its properties, and to study the implications for the stability of solitary waves. The algorithms reported here are developed in the exterior algebra representation, which leads to a robust and fast algorithm with some novel properties. We use two different representations for the Maslov index, one based on an intersection index and one based on approximating the homoclinic orbit by a sequence of periodic orbits. New results on the Maslov index for solitary wave solutions of reaction-diffusion equations, the fifth-order Korteweg-De Vries equation, and the longwave-shortwave resonance equations are presented. Part 1 considers the case of four-dimensional phase space, and Part 2 considers the case of $2n-$dimensional phase space with $n>2$.
Fichier principal
Vignette du fichier
Maslov_part1-4D.pdf (929.28 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00383888 , version 1 (13-05-2009)

Identifiants

Citer

Frédéric Chardard, Frédéric Dias, Thomas Bridges. Computational aspects of the Maslov index of solitary waves. 2009. ⟨hal-00383888⟩
440 Consultations
172 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More