2005/12/31 by Artur Sergyeyev, Dmitry Demskoi
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Conservation law #Flow (mathematics) #Hamiltonian (control theory) #Homogeneous space #Nonlinear Waves and Solitons #Nonlinear system #Operator (biology) #Quantum Mechanics and Non-Hermitian Physics #Recursion (computer science) #Symmetry (geometry) #Symplectic geometry #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1063/1.2710552
published as J.Math.Phys.48:042702,2007 · 16 pages, LaTeX 2e, no figures (in this version the recursion operator for the Sasa--Satsuma equation was written in a somewhat different form, several typos were fixed, and titles of the papers were added in the bibliography)
arxiv created 2007/02/26 · openalex publication_date 2007/04/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present a new symplectic structure and a hereditary recursion operator for the Sasa-Satsuma equation which is widely used in nonlinear optics. Using an integrodifferential substitution relating this equation to a third-order symmetry flow of the complex sine-Gordon II equation enabled us to find a hereditary recursion operator and higher Hamiltonian structures for the latter equation. We also show that both the Sasa-Satsuma equation and the third-order symmetry flow for the complex sine-Gordon II equation are bi-Hamiltonian systems, and we construct several hierarchies of local and nonlocal symmetries for these systems.