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Título:
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Vectorial Darboux transformations for the Kadomtsev-Petviashvili hierarchy
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Autores:
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Liu, Q. P. ;
Mañas Baena, Manuel
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Tipo de documento:
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texto impreso
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Editorial:
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Springer, 1999-03
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Dimensiones:
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application/pdf
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Nota general:
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info:eu-repo/semantics/openAccess
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Idiomas:
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Física: Física-Modelos matemáticos
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Materia = Ciencias: Física: Física matemática
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Tipo = Artículo
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Resumen:
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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.
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En línea:
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https://eprints.ucm.es/id/eprint/32483/1/ma%C3%B1as32preprint.pdf
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