4,142 research outputs found
The semi-discrete AKNS system: Conservation laws, reductions and continuum limits
In this paper, the semi-discrete Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy
is shown in spirit composed by the Ablowitz-Ladik flows under certain
combinations. Furthermore, we derive its explicit Lax pairs and infinitely many
conservation laws, which are non-trivial in light of continuum limit.
Reductions of the semi-discrete AKNS hierarchy are investigated to include the
semi-discrete Korteweg-de Vries (KdV), the semi-discrete modified KdV, and the
semi-discrete nonlinear Schr\"odinger hierarchies as its special cases.
Finally, under the uniform continuum limit we introduce in the paper, the above
results of the semi-discrete AKNS hierarchy, including Lax pairs, infinitely
many conservation laws and reductions, recover their counterparts of the
continuous AKNS hierarchy
Dibromido[(S)-2-(pyrrolidin-2-yl)-1H-benzimidazole]zinc(II)
The title compound, [ZnBr2(C11H13N3)], was synthesized by hydroÂthermal reaction of ZnBr2 and (S)-2-(pyrrolidin-2-yl)-1H-benzimidazole. The ZnII atom has a distorted tetraÂhedral geometry and is coordinated by two N atoms from the chelating organic ligand and two terminal Br− anions. In the crystal structure, molÂecules are linked into a chain along the [101] direction by N—H⋯Br and C—H⋯Br hydrogen bonds
Bis(nitrato-κO)[(S)-2-(pyrrolidin-2-yl)-1H-benzimidazole]cadmium(II)
The title compound, [Cd(NO3)2(C11H13N3)2], was synthesized by hydroÂthermal reaction of Cd(NO3)2 and S-2-(pyrrolidin-2-yl)-1H-1,3-benzimidazole. The Cd atom lies on an inversion centre. The distorted octaÂhedral Cd environment contains two planar trans-related N,N-chelating S-2-(pyrrolidin-2-yl)-1H-1,3-benzimidazole ligands in one plane and two monodentate nitrate ligands. N—H⋯O hydrogen bonds involving a nitrate O atom build up an infinite chain parallel to the a axis
The long-lasting optical afterglow plateau of short burst GRB 130912A
The short burst GRB 130912A was detected by Swift, Fermi satellites and
several ground-based optical telescopes. Its X-ray light curve decayed with
time normally. The optical emission, however, displayed a long term plateau,
which is the longest one in current short GRB observations. In this work we
examine the physical origin of the X-ray and optical emission of this peculiar
event. We find that the canonical forward shock afterglow emission model can
account for the X-ray and optical data self-consistently and the energy
injection model that has been widely adopted to interpret the
shallowly-decaying afterglow emission is not needed. We also find that the
burst was born in a very-low density interstellar medium, consistent with the
compact object merger model. Significant fractions of the energy of the forward
shock have been given to accelerate the non-thermal electrons and amplify the
magnetic fields (i.e., and , respectively), which are much larger than those inferred in most short
burst afterglow modeling and can explain why the long-lasting optical afterglow
plateau is rare in short GRBs.Comment: 5 pages, 2 figure
(S)-2-Ammonio-3-(4-nitroÂphenÂyl)propanoate monohydrate
The title compound, C9H10N2O4·H2O, exists as a zwitterion with a deprotonated carboxyl group and a protonated amino group. The crystal packing is stabilized by N—H⋯O and O—H⋯O hydrogen bonds, building sheets parallel to the (001) plane. The absolute configuration was deduced from the synthetic pathway
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