Computation of densities and fluxes of nonlinear differential‐difference equations

Computation of densities and fluxes of nonlinear differential‐difference equations

Direct methods to find conserved densities and fluxes of differential-difference equations are presented and illustrated for the Kac-van Moerbeke (KvM) and modified Volterra lattices. A Miura map which connects both lattices is explicitly constructed based on homotopic deformation. The map is used r...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2003-11, Vol.459 (2039), p.2705-2729
Hauptverfasser: Hickman, Mark S, Hereman, Willy A
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
College mathematics
Computer algebra systems
Conservation laws
Conserved Densities
DDEs
Difference equations
Duets
Flux density
Lattice
Lattice energy
Mathematical lattices
Miura Map
Nonlinear Chains
Semi-Discrete Lattices
Symmetry
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:Direct methods to find conserved densities and fluxes of differential-difference equations are presented and illustrated for the Kac-van Moerbeke (KvM) and modified Volterra lattices. A Miura map which connects both lattices is explicitly constructed based on homotopic deformation. The map is used recursively to compute conserved densities of the KvM lattice. The algorithms presented could be implemented in computer algebra systems and could be used to investigate the integrability of semi-discrete lattices.
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.2003.1151