Sasa-Satsuma (complex modified Korteweg–de Vries II) and the complex sine-Gordon II equation revisited: Recursion operators, nonlocal symmetries, and more
Sasa-Satsuma (complex modified Korteweg–de Vries II) and the complex sine-Gordon II equation revisited: Recursion operators, nonlocal symmetries, and more
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DOI：
10.1063/1.2710552
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发表时间：
2005-12
影响因子：
1.3
通讯作者：
Artur Sergyeyev;D. Demskoi
中科院分区：
文献类型：
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作者：
Artur Sergyeyev;D. Demskoi
对非线性光学中广泛应用的Sasa-Satsuma方程给出了一个新的辛结构和一个遗传递推算子。使用积分微分替换将该方程与复sine-Gordon II方程的三阶对称流联系起来，使我们能够找到后一个方程的遗传递归算子和更高的汉密尔顿结构。我们还证明了Sasa-Satsuma方程和复sine-Gordon II方程的三阶对称流都是双Hamilton系统，并且我们为这些系统构造了几个局部和非局部对称性的族.
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.