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Restricted Flows and the Soliton Equation with Self-Consistent Sources
The KdV equation is used as an example to illustrate the relation between the
restricted flows and the soliton equation with self-consistent sources.
Inspired by the results on the Backlund transformation for the restricted flows
(by V.B. Kuznetsov et al.), we constructed two types of Darboux transformations
for the KdV equation with self-consistent sources (KdVES). These Darboux
transformations are used to get some explicit solutions of the KdVES, which
include soliton, rational, positon, and negaton solutions.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on
Integrable Systems and Related Topics, published in SIGMA (Symmetry,
Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
Conductance through a single impurity in the metallic zigzag carbon nanotube
We investigate transport through a single impurity in metallic zigzag carbon
nanotube and find the conductance sensitively depends on the impurity strength
and the bias voltage. It is rather interesting that interplay between the
current-carrying scattering state and evanescent modes leads to rich phenomena
including resonant backward scattering, perfect tunneling and charge
accumulations. In addition, we also find a dual relation between the
backscattered conductance and the charge accumulation. At the end, relevance to
the experiments is discussed.Comment: 3 pages, 3 figure
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