De Sole, A., Kac, V. G. and Valeri, D. (2016) A new scheme of integrability for (bi)Hamiltonian PDE. Communications in Mathematical Physics, 347(2), pp. 449-488. (doi: 10.1007/s00220-016-2684-x)
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Abstract
We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, which combines the fractional powers technique of Gelfand and Dickey, and the classical Hamiltonian reduction technique of Drinfeld and Sokolov. The method is based on the notion of an Adler type matrix pseudodifferential operator and the notion of a generalized quasideterminant. We also introduce the notion of a dispersionless Adler type series, which is applied to the study of dispersionless Hamiltonian equations. Non-commutative Hamiltonian equations are discussed in this framework as well.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Valeri, Dr Daniele |
| Authors: | De Sole, A., Kac, V. G., and Valeri, D. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Communications in Mathematical Physics |
| Publisher: | Springer |
| ISSN: | 0010-3616 |
| ISSN (Online): | 1432-0916 |
| Published Online: | 08 June 2016 |
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