期刊
REVIEWS IN MATHEMATICAL PHYSICS
卷 30, 期 2, 页码 -出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0129055X18500034
关键词
Matrix spectral problem; integrable coupling; Darboux transformation; non-semisimple Lie algebra; soliton
资金
- NNSFC [11371326, 11271008, 11325417, 61227902, 61072147]
- NSF [DMS-1664561]
- 111 project of China [B16002]
- Natural Science Fund for Colleges and Universities of Jiangsu Province of China [17KJB110020]
- Natural Science Foundation of Shanghai [11ZR1414100]
- Zhejiang Innovation Project of China [T200905]
- Shanghai University Leading Academic Discipline Project [A.13-0101-12-004]
- Shanghai Second Polytechnic University
- China Scholarship Council
- University of South Florida
- Lanzhou University
- First-Class Discipline of Universities in Shanghai
- Shanghai University of Electric Power
A formulation of Darboux transformations is proposed for integrable couplings, based on non-semisimple matrix Lie algebras. Applications to a kind of integrable couplings of the AKNS equations are made, along with an explicit formula for the associated Backlund transformation. Exact one-soliton-like solutions are computed for the integrable couplings of the second- and third-order AKNS equations, and a type of reduction is created to generate integrable couplings and their one-soliton-like solutions for the NLS and MKdV equations.
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