Abstract
Based on the six-dimensional real special orthogonal Lie algebraSO(4), a new Lax integrable hierarchy is obtained by constructing an isospectral problem. Furthermore, we construct bi-integrable couplings for this hierarchy from the enlarged matrix spectral problems and the enlarged zero curvature equations. Hamiltonian structures of the obtained bi-integrable couplings are constructed by the variational identity.
Highlights
IntroductionIntegrable equations are a remarkable class of nonlinear equations
As is well known, integrable equations are a remarkable class of nonlinear equations
New Lax integrable hierarchy (14) is obtained by constructing an isospectral problem associated with SO(4)
Summary
Integrable equations are a remarkable class of nonlinear equations. It is always interesting to explore any new procedure for generating integrable couplings for different soliton hierarchies, even from existing nonsemisimple Lie algebras. The variational identity is proposed, which can be used to obtain the Hamiltonian structures in the case of nonsemisimple Lie algebras [5,6,7]. In [8], Ma et al propose a new way to generate integrable couplings through a few classes of matrix Lie algebras consisting of block matrices. Bi-integrable couplings of a new soliton hierarchy associated with SO(3) have been constructed [11]. Integrable couplings correspond to nonsemisimple Lie algebras g, and such Lie algebras can be written as semidirect sums [13]:. We will construct bi-integrable couplings associated with SO(4) for a new hierarchy from the enlarged matrix spectral problems and the enlarged zero curvature equations. Our work is essentially motivated by [11, 14, 15]
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