Abstract
Based on the three-dimensional real special orthogonal Lie algebraso(3,R), we construct a new hierarchy of soliton equations by zero curvature equations and show that each equation in the resulting hierarchy has a bi-Hamiltonian structure and thus integrable in the Liouville sense. Furthermore, we present the infinitely many conservation laws for the new soliton hierarchy.
Highlights
Conservation laws are widespread in applied mathematics, which reflect a phenomenon that some physical quantities do not change with time
The algebra so(3, R) contains matrices of the form λme1 + λne2 + λle3 with arbitrary integers m, n, l. This matrix loop algebra lays a foundation for our study of soliton equations
This isospectral problem is of the same type as the BroerKaup-Kupershmidt one [16], but its underlying loop algebra is different
Summary
Conservation laws are widespread in applied mathematics, which reflect a phenomenon that some physical quantities do not change with time In soliton theory, they play an important role in the study of integrability of soliton equations. The algebra so(3, R) contains matrices of the form λme1 + λne2 + λle with arbitrary integers m, n, l This matrix loop algebra lays a foundation for our study of soliton equations. We would like to from a spectral problem, based on the matrix loop algebra so(3, R), and construct a new soliton hierarchy from associated zero curvature equations. The trace identity is used to furnish the corresponding Hamiltonian structures and so all equations in the resulting soliton hierarchy are Liouville integrable. We introduce two variables E and F to construct conservation laws of the equation hierarchy and the first two conserved densities and fluxes are listed
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