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The D-bar method, inversion of certain integrals and integrability in 4 + 2 and 3 + 1 dimensions.
- Source :
-
Journal of Physics A: Mathematical & Theoretical . Aug2008, Vol. 41 Issue 34, p344006-344006. 1p. - Publication Year :
- 2008
-
Abstract
- We first review a method for deriving linear and nonlinear transform pairs, which is based on the spectral analysis of an eigenvalue equation and on the formulation of a d-bar problem. Then, we present two applications of this method: (a) we derive a certain linear transform pair in one dimension, which appears in the characterization of the Dirichlet-to-Neumann map of the Laplace equation in the interior of a convex two-dimensional curvilinear domain. (b) We derive a nonlinear Fourier transform pair in four dimensions, which can be used for the solution of the Cauchy problem of an integrable generalization of the Kadomtsev-Petviashvilli equation in 4 + 2, i.e. in four spatial and two temporal dimensions. The question of reducing this equation form 4 + 2 to 3 + 1 dimensions is also discussed. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 17518113
- Volume :
- 41
- Issue :
- 34
- Database :
- Academic Search Index
- Journal :
- Journal of Physics A: Mathematical & Theoretical
- Publication Type :
- Academic Journal
- Accession number :
- 44637033
- Full Text :
- https://doi.org/10.1088/1751-8113/41/34/344006