22,313 research outputs found
Dressing method and the coupled KP hierarchy
The coupled KP hierarchy, introduced by Hirota and Ohta, are investigated by
using the dressing method. It is shown that the coupled KP hierarchy can be
reformulated as a reduced case of the 2-component KP hierarchy.Comment: 11 pages, LaTeX, no figure
Bilinearization of Discrete Soliton Equations and Singularity Confinement
Bilinear forms for some nonlinear partial difference equations(discrete
soliton equations) are derived based on the results of singularity confinement.
Using the bilinear forms, the N-soliton and algebraic solutions of the discrete
potential mKdV equation are constructed.Comment: 14 pages, LaTe
Constructing a Supersymmetric Integrable System from the Hirota Method in Superspace
An N=1 supersymmetric system is constructed and its integrability is shown by
obtaining three soliton solutions for it using the supersymmetric version of
Hirota's direct method.Comment: 10 pages, no figure
Geometric quantization of Dirac manifolds
We define prequantization for Dirac manifolds to generalize known procedures
for Poisson and (pre) symplectic manifolds by using characteristic
distributions obtained from 2-cocycles associated to Dirac structures. Given a
Dirac manifold , we construct Poisson structure on the space of
admissible functions on and a representation of the Poisson algebra to
establish the prequantization condition of in terms of a Lie algebroid
cohomology. Additional to this, we introduce a polarization for a Dirac
manifold and discuss procedures for quantization in two cases where is
compact and where is not compact.Comment: 33 pages. errors and typos correcte
- …