Abstract
Hamiltonian structures of integrable nonlinear evolution equations are studied in the framework of infinite dimensional Lie Algebra. We have shown that it is actually possible to derive the two-symplectic structures from the formalism of G. Zhang Tu. Furthermore we have extended this formalism to a system with 3 × 3 matrix structure. An important aspect of our formulation is to implement reduction mechanism to arrive at a specific nonlinear system. As examples we have discussed the cases of KdV, Langmuir solitons.
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Roy, S., Roy Chowdhury, A. (1990). Lie Algebra, Bi-Hamiltonian Structure and Reduction Problem for Integrable Nonlinear Systems. In: Lakshmanan, M., Daniel, M. (eds) Symmetries and Singularity Structures. Research Reports in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76046-4_5
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DOI: https://doi.org/10.1007/978-3-642-76046-4_5
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