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| BINARY NONLINEARIZATION FOR THE DIRAC SYSTEMS |
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Citation： |
Ma Wenxiu.BINARY NONLINEARIZATION FOR THE DIRAC SYSTEMS[J].Chinese Annals of Mathematics B,1997,18(1):79~88 |
| Page view： 1119
Net amount： 902 |
Authors： |
Ma Wenxiu; |
Foundation： |
Project supported by the National Natural Science
Foundation of China |
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| Abstract： |
A Bargmann symmetry constraint is proposed for the Lax pairs and the
adjoint Lax pairs of the Dirac systems. It is shown that the spatial
part of the nonlinearized Lax pairs and adjoint Lax pairs is a finite
dimensional Liouville integrable Hamiltonian system and that under the control
of the spatial part, the time parts of
the nonlinearized Lax pairs and adjoint Lax pairs are interpreted as a hierarchy
of commutative, finite dimensional Liouville integrable Hamiltonian systems
whose Hamiltonian functions consist of a series of integrals of
motion for the spatial part. Moreover an involutive representation of
solutions of the Dirac systems exhibits their integrability by
quadratures. This kind of symmetry constraint procedure involving the
spectral problem and the adjoint spectral problem is referred to as a
binary nonlinearization technique like a binary Darboux transformation. |
Keywords： |
Zero curvature representation, Nonlinerization
method, Liouville integrable system, Soliton hierarchy |
Classification： |
35Q51, 35Q58, 58F05 |
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