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Liu, Q. P. and Mañas Baena, Manuel
(1999)
*Vectorial Darboux transformations for the Kadomtsev-Petviashvili hierarchy.*
Journal of nonlinear science, 9
(2).
pp. 213-232.
ISSN 0938-8974

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Official URL: http://dx.doi.org/10.1007/s003329900070

## Abstract

We consider the vectorial approach to the binary Darboux transformations for the Kadomtsev-Petviashvili hierarchy in its Zakharov-Shabat formulation. We obtain explicit formulae for the Darboux transformed potentials in terms of Grammian type determinants. We also study the n-th Gel'fand-Dickey hierarchy introducing spectral operators and obtaining similar results. We reduce the above-mentioned results to the Kadomtsev-Petviashvili I and II real forms, obtaining corresponding vectorial Darboux transformations. In particular for the Kadomtsev-Petviashvili I hierarchy, we get the line soliton, the lump solution, and the Johnson-Thompson lump, and the corresponding determinant formulae for the nonlinear superposition of several of them. For Kadomtsev-Petviashvili II apart from the line solitons, we get singular rational solutions with its singularity set describing the motion of strings in the plane. We also consider the I and II real forms for the Gel'fand-Dickey hierarchies obtaining the vectorial Darboux transformation in both cases.

Item Type: | Article |
---|---|

Additional Information: | ©Springer. |

Uncontrolled Keywords: | Time-dependent schrodinger; Inverse scattering transform; Rational solutions; Davey-stewartson; Gauge transformations; Jacobian varieties; Soliton-equations; Kp hierarchy; Evolution; Systems |

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

ID Code: | 32483 |

Deposited On: | 23 Jul 2015 10:46 |

Last Modified: | 10 Dec 2018 15:10 |

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