Sasa-Satsuma (complex modified Korteweg-de Vries II) and the complex sine-Gordon II equation revisited: Recursion operators, nonlocal symmetries, and more

Artur Sergyeyev, Dmitry Demskoi

Research output: Contribution to journalArticle

18 Citations (Scopus)
14 Downloads (Pure)

Abstract

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
Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalJournal of Mathematical Physics
Volume48
Issue number4
DOIs
Publication statusPublished - Apr 2007

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