RT Journal Article
T1 Vectorial Darboux transformations for the Kadomtsev-Petviashvili hierarchy
A1 Liu, Q. P.
A1 Mañas Baena, Manuel Enrique
AB 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.
PB Springer
SN 0938-8974
YR 1999
FD 1999-03
LK https://hdl.handle.net/20.500.14352/59691
UL https://hdl.handle.net/20.500.14352/59691
LA eng
NO ©Springer.
DS Docta Complutense
RD 18 abr 2025