NDLI: The n × n KdV hierarchy

Content Provider	Springer Nature Link
Author	Terng, Chuu Lian Uhlenbeck, Karen
Copyright Year	2011
Abstract	We introduce two new soliton hierarchies that are generalizations of the KdV hierarchy. Our hierarchies are restrictions of the AKNS n × n hierarchy coming from two unusual splittings of the loop algebra. These splittings come from automorphisms of the loop algebra instead of automorphisms of $${sl (n, \mathbb{C})}$$ . The flows in the hierarchy include systems of coupled nonlinear Schrödinger equations. Since they are constructed from a Lie algebra splitting, the general method gives formal inverse scattering, bi-Hamiltonian structures, commuting flows, and Bäcklund transformations for these hierarchies.
Starting Page	37
Ending Page	61
Page Count	25
File Format	PDF
ISSN	16617738
Journal	Journal of Fixed Point Theory and Applications
Volume Number	10
Issue Number	1
e-ISSN	16617746
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2011-08-04
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Soliton hierarchy Lie algebra splitting KdV-type equations Relations with infinite-dimensional Lie algebras and other algebraic structures Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies Mathematics Mathematical Methods in Physics Analysis
Content Type	Text
Resource Type	Article
Subject	Geometry and Topology Applied Mathematics Modeling and Simulation

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The n × n KdV hierarchy