Abstract
In this paper, we mainly give the Lie algebras E, F and H of three kinds and their commutator, respectively. Next, we establish three isospectral problems with the help of their corresponding loop algebras Ẽ, F̃, and H̃. Based on on the Tu scheme, coupling integrable couplings of three kinds for the generalized coupled Burgers equation hierarchy are obtained. Finally, we obtain the Hamiltonian structure of one of the coupling integrable couplings of the generalized coupled Burgers equation hierarchy by using the quadratic-form identity.
Highlights
The development of soliton theory has undergone a rapid development in the 1960s
Zhang even proposed an efficient method for constructing nonlinear evolution equations and their resulting Hamiltonian structure
Hu developed the trace identity, and got an efficient method to work out the soliton equations and the Hamiltonian structure
Summary
The development of soliton theory has undergone a rapid development in the 1960s. Integrable couplings are a new important and interesting topic in the field of soliton theory [1– 3]. Inc, Yusuf, Aliyu and Baleanu discussed a Lie symmetry analysis and conservation laws for the time fractional simplified modified Kawahara equation, the generalized shallow water wave equation, the time fractional dispersive long-wave equation and the time fractional generalized Burgers–Huxley equation They studied a time fractional thirdorder variant Boussinesq system and gave a symmetry analysis, explicit solutions, conservation laws and numerical approximations [32–37]. Zhang even proposed an efficient method for constructing nonlinear evolution equations and their resulting Hamiltonian structure. The one coupling integrable coupling of the generalized coupled Burgers equation hierarchy has a Hamiltonian structure obtained by employing the quadratic-form identity [39]
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