Three New (2+1)-dimensional Integrable Systems and Some Related Darboux Transformations
| Autor: | Xiu-Rong Guo |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Physics and Astronomy (miscellaneous) Integrable system 010102 general mathematics One-dimensional space Zero (complex analysis) 01 natural sciences 010305 fluids & plasmas Nonlinear system Matrix (mathematics) Nonlinear Sciences::Exactly Solvable and Integrable Systems Operator (computer programming) 0103 physical sciences Lie algebra Heat equation 0101 mathematics Mathematics |
| Zdroj: | Communications in Theoretical Physics. 65:735-742 |
| ISSN: | 0253-6102 |
| DOI: | 10.1088/0253-6102/65/6/735 |
| Popis: | We introduce two operator commutators by using different-degree loop algebras of the Lie algebra A1, then under the framework of zero curvature equations we generate two (2+1)-dimensional integrable hierarchies, including the (2+1)-dimensional shallow water wave (SWW) hierarchy and the (2+1)-dimensional Kaup-Newell (KN) hierarchy. Through reduction of the (2+1)-dimensional hierarchies, we get a (2+1)-dimensional SWW equation and a (2+1)-dimensional KN equation. Furthermore, we obtain two Darboux transformations of the (2+1)-dimensional SWW equation. Similarly, the Darboux transformations of the (2+1)-dimensional KN equation could be deduced. Finally, with the help of the spatial spectral matrix of SWW hierarchy, we generate a (2+1) heat equation and a (2+1) nonlinear generalized SWW system containing inverse operators with respect to the variables x and y by using a reduction spectral problem from the self-dual Yang-Mills equations. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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