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Guil Guerrero, Francisco and Mañas Baena, Manuel
(1994)
*AKNS hierarchy, self-similarity, string equations and the Grassmannian.*
Journal of physics A-Mathematical and General, 27
(6).
pp. 2129-2142.
ISSN 0305-4470

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Official URL: http://dx.doi.org/10.1088/0305-4470/27/6/034

## Abstract

In this paper the Galilean, scaling and translational self-similarity conditions for the AKNS hierarchy are analysed geometrically in terms of the infinite-dimensional Grassmannian. The string equations of the one-matrix model correspond to the Galilean self-similarity condition for this hierarchy. We describe, in terms of the initial data for the zero-curvature 1 -form of the AKNS hierarchy, the moduli space of these self-similar solutions in the Sato Grassmannian. As a by-product we characterize the points in the Segal-Wilson Grassmannian corresponding to the Sachs rational solutions of the AKNS equation and to the Nakamura-Hirota rational solutions of the NLS equation.

Item Type: | Article |
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Additional Information: | ©IOP Publishing LTD. |

Uncontrolled Keywords: | Ordinary differential-equations; Rational coefficients; Tau-function; Deformation; Algebras |

Subjects: | Sciences > Physics > Physics-Mathematical models Sciences > Physics > Mathematical physics |

ID Code: | 32527 |

Deposited On: | 27 Jul 2015 09:39 |

Last Modified: | 10 Dec 2018 15:10 |

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