dorsal/arxiv
View SchemaBinary nonlinearization for the Dirac systems
| Authors | Wen-Xiu Ma |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9512002 |
| URL | https://arxiv.org/abs/solv-int/9512002 |
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.
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"abstract": "A Bargmann symmetry constraint is proposed for the Lax pairs and the adjoint\nLax pairs of the Dirac systems. It is shown that the spatial part of the\nnonlinearized Lax pairs and adjoint Lax pairs is a finite dimensional Liouville\nintegrable Hamiltonian system and that under the control of the spatial part,\nthe time parts of the nonlinearized Lax pairs and adjoint Lax pairs are\ninterpreted as a hierarchy of commutative, finite dimensional Liouville\nintegrable Hamiltonian systems whose Hamiltonian functions consist of a series\nof integrals of motion for the spatial part. Moreover an involutive\nrepresentation of solutions of the Dirac systems exhibits their integrability\nby quadratures. This kind of symmetry constraint procedure involving the\nspectral problem and the adjoint spectral problem is referred to as a binary\nnonlinearization technique like a binary Darboux transformation.",
"arxiv_id": "solv-int/9512002",
"authors": [
"Wen-Xiu Ma"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "Binary nonlinearization for the Dirac systems",
"url": "https://arxiv.org/abs/solv-int/9512002"
},
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