Journal of Applied Nonlinear Dynamics
A Few Notes on Lax Integrability, Integrable Couplings and Computing Formula of the Constant γ
Journal of Applied Nonlinear Dynamics 1(4) (2012) 401--406 | DOI:10.5890/JAND.2012.06.003
F.K. Guo$^{1}$, B.L. Feng$^{2}$, T.T. Guo$^{3}$
$^{1}$ Information School, Shandong University of Science and Technology, Qingdao 266510, China
$^{2}$ School of Mathematics and Information Sciences, Weifang University, Weifang 261061, China
$^{3}$ Business College of Shanxi University, Taiyuan 030031, China
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Abstract
We point out in the paper that the current available definition on Lax integrability is necessary to be modified; the existed method for generating integrable couplings by the approach “original equations + symmetric equations” is wrong. Besides, a simple and efficient formula for calculating the constant γ appearing in the trace identity and the quadratic-form identity is proposed, which is universal for finding Hamiltonian structures of integrable dynamics.
References
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