期刊
JOURNAL OF MATHEMATICAL PHYSICS
卷 41, 期 11, 页码 7769-7782出版社
AMER INST PHYSICS
DOI: 10.1063/1.1314895
关键词
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A spectral problem and the associated Gerdjikov-Ivanov (GI) hierarchy of nonlinear evolution equations is presented. As a reduction, the well-known GI equation of derivative nonlinear Schrodinger equations is obtained. It is shown that the GI hierarchy is integrable in a Liouville sense and possesses bi-Hamiltonian structure. Moreover, the spectral problem can be nonlinearized as a finite dimensional completely integrable system under the Bargmann constraint between the potentials and the eigenfunctions. In particular, an explicit N-fold Darboux transformation for the GI equation is constructed with the help of a gauge transformation of spectral problems and a reduction technique. Some explicit solitonlike solutions of the GI equation are given by applying its Darboux transformation. (C) 2000 American Institute of Physics. [S0022- 2488(00)01611-X].
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