Tau functions for matrix hierarchies.
| dc.contributor.advisor | Dickey, Leonid, | en_US |
| dc.contributor.author | Vasilev, Stanislav H. | en_US |
| dc.date.accessioned | 2013-08-16T12:29:31Z | |
| dc.date.available | 2013-08-16T12:29:31Z | |
| dc.date.issued | 1997 | en_US |
| dc.description.abstract | The totality of all zero curvature equations with a rational dependence of connection matrices on a spectral parameter form a hierarchy, which means that all the corresponding vector fields commute. This is the so-called General Zakharov Shabat (GZS) hierarchy. We consider a subhierarchy of GZS with a given fixed set of poles. The "time variables" depend on three indices, one refers to a chosen pole, the other is a vector index taking values from 1 to n where n is a dimension of the matrices, and the third one corresponds to the order of the pole. In the case of a single pole, the subhierarchy is a generalization of the AKNS hierarchy with matrices of arbitrary dimension and a pole of arbitrary order. | en_US |
| dc.description.abstract | The goal of the work is two-fold. First, we want to construct Grassmannian tau-functions for GZS. We present such a construction for its diagonal tau-functions. Second, we want to give an algebraic-geometrical construction of the Baker and tau-functions with a formula connecting them. We have considered the general case when the cross-poles equations are taken into account. | en_US |
| dc.format.extent | vi, 46 leaves ; | en_US |
| dc.identifier.uri | http://hdl.handle.net/11244/5429 | |
| dc.note | Adviser: Leonid Dickey. | en_US |
| dc.note | Source: Dissertation Abstracts International, Volume: 58-01, Section: B, page: 0234. | en_US |
| dc.subject | Differential equations. | en_US |
| dc.subject | Nonlinear theories. | en_US |
| dc.subject | Grassman manifolds. | en_US |
| dc.subject | Mathematics. | en_US |
| dc.subject | Solitons. | en_US |
| dc.thesis.degree | Ph.D. | en_US |
| dc.thesis.degreeDiscipline | Department of Mathematics | en_US |
| dc.title | Tau functions for matrix hierarchies. | en_US |
| dc.type | Thesis | en_US |
| ou.group | College of Arts and Sciences::Department of Mathematics | |
| ou.identifier | (UMI)AAI9719904 | en_US |
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