21,149 research outputs found
Bright-dark mixed -soliton solutions of the multi-component Mel'nikov system
By virtue of the KP hierarchy reduction technique, we construct the general
bright-dark mixed -soliton solution to the multi-component Mel'nikov system
comprised of multiple (say ) short-wave components and one long-wave
component with all possible combinations of nonlinearities including
all-positive, all-negative and mixed types. Firstly, the two-bright-one-dark
(2-b-1-d) and one-bright-two-dark (1-b-2-d) mixed -soliton solutions in
short-wave components of the three-component Mel'nikov system are derived in
detail. Then we extend our analysis to the -component Mel'nikov system to
obtain its general mixed -soliton solution. The formula obtained unifies the
all-bright, all-dark and bright-dark mixed -soliton solutions. For the
collision of two solitons, the asymptotic analysis shows that for a
-component Mel'nikov system with , inelastic collision takes
place, resulting in energy exchange among the short-wave components supporting
bright solitons only if the bright solitons appear at least in two short-wave
components. Whereas, the dark solitons in the short-wave components and the
bright solitons in the long-wave component always undergo elastic collision
which just accompanied by a position shift.Comment: arXiv admin note: substantial text overlap with arXiv:1706.0549
Scaling of Coulomb pseudo-potential in s-wave narrow-band superconductors
The Coulomb pseudo-potential is extracted by fitting the numerically
calculated transition temperature of the Eliashberg-Nambu equation which
is extended to incorporate the narrow-band effects, that is, the vertex
correction and the frequency dependence of the screened Coulomb interaction. It
is shown that even for narrow-band superconductors, where the fermi energy is comparable with the phonon frequency , the Coulomb
pseudo-potential is a pertinent parameter, and is still given by , provided is
appropriately scaled.Comment: 5 pages, 3 figures, accepted for publication by Phys. Rev.
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