The constrained modified KP hierarchy and the generalized Miura transformations

In this letter, we consider the second Hamiltonian structure of the constrained modified KP hierarchy. After mapping the Lax operator to a pure differential operator the second structure becomes the sum of the second and the third Gelfand-Dickey brackets defined by this differential operator. We simplify this Hamiltonian structure by factorizing the Lax operator into linear terms.Comment: 8 pages, latex, no figure

A Note on the Gauge Equivalence between the Manin-Radul and Laberge-Mathieu Super KdV Hierarchies

The gauge equivalence between the Manin-Radul and Laberge-Mathieu super KdV hierarchies is revisited. Apart from the Inami-Kanno transformation, we show that there is another gauge transformation which also possess the canonical property. We explore the relationship of these two gauge transformations from the Kupershmidt-Wilson theorem viewpoint and, as a by-product, obtain the Darboux-Backlund transformation for the Manin-Radul super KdV hierarchy. The geometrical intepretation of these transformations is also briefly discussed.Comment: 8 pages, revtex, 1 figur

B\"{a}cklund transformations for the KP and mKP hierarchies with self-consistent sources

Using gauge transformations for the corresponding generating pseudo-differential operators $L^n$ in terms of eigenfunctions and adjoint eigenfunctions, we construct several types of auto-B\"{a}cklund transformations for the KP hierarchy with self-consistent sources (KPHSCS) and mKP hierarchy with self-consistent sources (mKPHSCS) respectively. The B\"{a}cklund transformations from the KPHSCS to mKPHSCS are also constructed in this way.Comment: 22 pages. to appear in J.Phys.

Spectrum of an oscillator with jumping frequency and the interference of partial susceptibilities

We study an underdamped oscillator with shot-noise frequency fluctuations. The oscillator spectrum is determined by the interference of the susceptibilities for different eigenfrequencies. Depending on the parameters, it has a fine structure or displays a single asymmetric peak. For nano-mechanical resonators with a fluctuating number of attached molecules, the spectrum is found in a simple analytical form. The results bear on various types of systems where the reciprocal correlation time of frequency fluctuations can be comparable to the typical frequency jumps

Nonuniform Self-Organized Dynamical States in Superconductors with Periodic Pinning

We consider magnetic flux moving in superconductors with periodic pinning arrays. We show that sample heating by moving vortices produces negative differential resistivity (NDR) of both N and S type (i.e., N- and S-shaped) in the voltage-current characteristic (VI curve). The uniform flux flow state is unstable in the NDR region of the VI curve. Domain structures appear during the NDR part of the VI curve of an N type, while a filamentary instability is observed for the NDR of an S type. The simultaneous existence of the NDR of both types gives rise to the appearance of striking self-organized (both stationary and non-stationary) two-dimensional dynamical structures.Comment: 4 pages, 2 figure

On the Miura map between the dispersionless KP and dispersionless modified KP hierarchies

We investigate the Miura map between the dispersionless KP and dispersionless modified KP hierarchies. We show that the Miura map is canonical with respect to their bi-Hamiltonian structures. Moreover, inspired by the works of Takasaki and Takebe, the twistor construction of solution structure for the dispersionless modified KP hierarchy is given.Comment: 19 pages, Latex, no figure

Molecular Gas in Candidate Double-Barred Galaxies II. Cooler, Less Dense Gas Associated with Stronger Central Concentrations

We have performed a multi-transition CO study of the centers of seven double-barred galaxies that exhibit a variety of molecular gas morphologies to determine if the molecular gas properties are correlated with the nuclear morphology and star forming activity. Near infrared galaxy surveys have revealed the existence of nuclear stellar bars in a large number of barred or lenticular galaxies. High resolution CO maps of these galaxies exhibit a wide range of morphologies. Recent simulations of double-barred galaxies suggest that variations in the gas properties may allow it to respond differently to similar gravitational potentials. We find that the 12CO J=3-2/J=2-1 line ratio is lower in galaxies with centrally concentrated gas distributions and higher in galaxies with CO emission dispersed around the galactic center in rings and peaks. The 13CO/12CO J=2-1 line ratios are similar for all galaxies, which indicates that the J=3-2/J=2-1 line ratio is tracing variations in gas temperature and density, rather than variations in optical depth. There is evidence that the galaxies which contain more centralized CO distributions are comprised of molecular gas that is cooler and less dense. Observations suggest that the star formation rates are higher in the galaxies containing the warmer, denser, less centrally concentrated gas. It is possible that either the bar dynamics are responsible for the variety of gas distributions and densities (and hence the star formation rates) or that the star formation alone is responsible for modifying the gas properties.Comment: 27 pages + 6 figures; to appear in the April 20, 2003 issue of Ap

Retrieving Bulge and Disk Parameters and Asymptotic Magnitudes from the Growth Curves of Galaxies

We show that the growth curves of galaxies can be used to determine their bulge and disk parameters and bulge-to-total luminosity ratios, in addition to their conventional asymptotic magnitudes, provided that the point spread function is accurately known and signal-to-noise ratio is modest (S/N$\gtrsim30$). The growth curve is a fundamental quantity that most future large galaxy imaging surveys will measure. Bulge and disk parameters retrieved from the growth curve will enable us to perform statistical studies of luminosity structure for a large number of galaxies.Comment: 28 pages including 13 PS figures; accepted for publication in PAS

B\"{a}cklund transformations for the constrained dispersionless hierarchies and dispersionless hierarchies with self-consistent sources

The B\"{a}cklund transformations between the constrained dispersionless KP hierarchy (cdKPH) and the constrained dispersionless mKP hieararchy (cdmKPH) and between the dispersionless KP hieararchy with self-consistent sources (dKPHSCS) and the dispersionless mKP hieararchy with self-consistent sources (dmKPHSCS) are constructed. The auto-B\"{a}cklund transformations for the cdmKPH and for the dmKPHSCS are also formulated.Comment: 11 page