905 research outputs found
Mismatch of conductivity anisotropy in the mixed and normal states of type-II superconductors
We have calculated the Bardeen-Stephen contribution to the vortex viscosity
for uniaxial anisotropic superconductors within the time-dependent
Ginzburg-Landau (TDGL) theory. We focus our attention on superconductors with a
mismatch of anisotropy of normal and superconducting characteristics. Exact
asymptotics for the Bardeen-Stephen contribution have been derived in two
limits: the cases of small and large electric field penetration depth (as
compared to the coherence length). Also we suggest a variational procedure
which allows us to calculate the vortex viscosity for superconductors with
arbitrary ratio of the coherence lenght to the electric field penetration
depth. The approximate analytical result is compared with numerical
calculations. Finally, using a generalized TDGL theory, we prove that the
viscosity anisotropy and, thus, the flux-flow conductivity anisotropy may
depend on temperature.Comment: 11 pages, 3 figures; typos corrected in Figs. 2 and
A new extended KP hierarchy
A method is proposed to construct a new extended KP hierarchy, which includes
two types of KP equation with self-consistent sources and admits reductions to
k-constrained KP hierarchy and to Gelfand-Dickey hierarchy with sources. It
provides a general way to construct soliton equations with sources and their
Lax representations.Comment: Published in Phys. Lett. A, 13 page
Generalized Darboux transformations for the KP equation with self-consistent sources
The KP equation with self-consistent sources (KPESCS) is treated in the
framework of the constrained KP equation. This offers a natural way to obtain
the Lax representation for the KPESCS. Based on the conjugate Lax pairs, we
construct the generalized binary Darboux transformation with arbitrary
functions in time for the KPESCS which, in contrast with the binary Darboux
transformation of the KP equation, provides a non-auto-B\"{a}cklund
transformation between two KPESCSs with different degrees. The formula for
N-times repeated generalized binary Darboux transformation is proposed and
enables us to find the N-soliton solution and lump solution as well as some
other solutions of the KPESCS.Comment: 20 pages, no figure
Negaton and Positon solutions of the soliton equation with self-consistent sources
The KdV equation with self-consistent sources (KdVES) is used as a model to
illustrate the method. A generalized binary Darboux transformation (GBDT) with
an arbitrary time-dependent function for the KdVES as well as the formula for
-times repeated GBDT are presented. This GBDT provides non-auto-B\"{a}cklund
transformation between two KdV equations with different degrees of sources and
enable us to construct more general solutions with arbitrary -dependent
functions. By taking the special -function, we obtain multisoliton,
multipositon, multinegaton, multisoliton-positon, multinegaton-positon and
multisoliton-negaton solutions of KdVES. Some properties of these solutions are
discussed.Comment: 13 pages, Latex, no figues, to be published in J. Phys. A: Math. Ge
Exponentially Localized Solutions of Mel'nikov Equation
The Mel'nikov equation is a (2+1) dimensional nonlinear evolution equation
admitting boomeron type solutions. In this paper, after showing that it
satisfies the Painlev\'{e} property, we obtain exponentially localized dromion
type solutions from the bilinearized version which have not been reported so
far. We also obtain more general dromion type solutions with spatially varying
amplitude as well as induced multi-dromion solutions.Comment: 12 pages, 2 figures, to appear in Chaos, Solitons and Fractal
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