Vectorial Darboux Transformations for the Kadomtsev-Petviashvili Hierarchy

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dc.creatorLiu, Q. P.
dc.creatorManas, M.
dc.date1997-05-21
dc.date1998-05-26
dc.date.accessioned2026-07-07T09:09:06Z
dc.date.available2026-07-07T09:09:06Z
dc.descriptionWe 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 non-linear 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.
dc.description26 pages, some formulae corrected. To appear in J. Nonlin. Sci
dc.identifierhttps://arxiv.org/abs/solv-int/9705012
dc.identifierhttp://arxiv.org/abs/solv-int/9705012
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/150951
dc.subjectExactly Solvable and Integrable Systems
dc.subjectHigh Energy Physics - Theory
dc.titleVectorial Darboux Transformations for the Kadomtsev-Petviashvili Hierarchy
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