2002/08/23 by J. C. Brunelli, A. Constandache, Ashok Das · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #hep-th #nlin.SI
paper · pdf · doi:10.1016/s0370-2693(02)02663-1
published as Phys.Lett.B546:167-176,2002 · Latex, 13 pages
arxiv created 2002/08/23 · openalex publication_date 2002/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a Lax equation for the non-linear sigma model which leads directly to the conserved local charges of the system. We show that the system has two infinite sets of such conserved charges following from the Lax equation, much like dispersionless systems. We show that the system has two Hamiltonian structures which are compatible so that it is truly a bi-Hamiltonian system. However, the two Hamiltonian structures act on the two distinct sets of charges to give the dynamical equations, which is quite distinct from the behavior in conventional integrable systems. We construct two recursion operators which connect the conserved charges within a given set as well as between the two sets. We show explicitly that the conserved charges are in involution with respect to either of the Hamiltonian structures thereby proving complete integrability of the system. Various other interesting features are also discussed.