Lie Algebraic Approach to Nonlinear Integrable Couplings of Evolution Type

Yufeng Zhang, Wen-Xiu Ma
2012 Journal of Applied Nonlinear Dynamics  
Based on two higher-dimensional extensions of Lie algebras, three kinds of specific Lie algebras are introduced. Upon constructing proper loop algebras, six isospectral matrix spectral problems are presented and they yield nonlinear integrable couplings of the Ablowitz-Kaup-Newell-Segur hierarchy, the Broer-Kaup hierarchy and the Kaup-Newell hierarchy. Especially, the reduced cases of the resulting integrable couplings give nonlinear integrable couplings of the nonlinear Schrödinger equation
more » ... the classical Boussinesq equation. Two linear functionals are introduced on two loop algebras of dimension 6 and Hamiltonian structures of the obtained nonlinear integrable couplings are worked out by employing the associated variational identity. The proposed approach can also be used to generate nonlinear integrable couplings for other integrable hierarchies.
doi:10.5890/jand.2011.12.001 fatcat:u7inkgdjmnfuhemw5bhbxafupy