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Dispersion managed solitons in the presence of saturated nonlinearity
Hundertmark, D.,Lee, Y.R.,Ried, T.,Zharnitsky, V. North-Holland 2017 Physica. D, Nonlinear phenomena Vol.356 No.-
The averaged dispersion managed nonlinear Schrodinger equation with saturated nonlinearity is considered. It is shown that under rather general assumptions on the saturated nonlinearity, the ground state solution corresponding to the dispersion managed soliton can be found for both zero residual dispersion and positive residual dispersion. The same applies to diffraction management solitons, which are a discrete version describing certain waveguide arrays.
Solitary waves in nonlocal NLS with dispersion averaged saturated nonlinearities
Hundertmark, Dirk,Lee, Young-Ran,Ried, Tobias,Zharnitsky, Vadim Elsevier 2018 Journal of differential equations Vol.265 No.8
<P><B>Abstract</B></P> <P>A nonlinear Schrödinger equation (NLS) with dispersion averaged nonlinearity of saturated type is considered. Such a nonlocal NLS is of integro-differential type and it arises naturally in modeling fiber-optics communication systems with periodically varying dispersion profile (dispersion management). The associated constrained variational principle is shown to posses a ground state solution by constructing a convergent minimizing sequence through the application of a method similar to the classical concentration compactness principle of Lions. One of the obstacles in applying this variational approach is that a saturated nonlocal nonlinearity does not satisfy uniformly the so-called strict sub-additivity condition. This is overcome by applying a special version of Ekeland's variational principle.</P>
On Dispersion Managed Solitons
Dirk Hundertmark,Young-Ran Lee 한국산업응용수학회 2008 한국산업응용수학회 학술대회 논문집 Vol.4 No.3
We give a brief survey on dispersion managed non-linear Schrodinger equation which is used in fiber optics communications.
<i>SPITZER</i>PARALLAX OF OGLE-2015-BLG-0966: A COLD NEPTUNE IN THE GALACTIC DISK
Street, R. A.,Udalski, A.,Novati, S. Calchi,Hundertmark, M. P. G.,Zhu, W.,Gould, A.,Yee, J.,Tsapras, Y.,Bennett, D. P.,Jørgensen, U. G.,Dominik, M.,Andersen, M. I.,Bachelet, E.,Bozza, V.,Bramich, D. M American Astronomical Society 2016 The Astrophysical journal Vol.819 No.2
<P>We report the detection of a cold Neptune m(planet) = 21 +/- 2M(circle plus) orbiting a 0.38M(circle dot) M dwarf lying 2.5-3.3 kpc toward the Galactic center as part of a campaign combining ground-based and Spitzer observations to measure the Galactic distribution of planets. This is the first time that the complex real-time protocols described by Yee et al., which aim to maximize planet sensitivity while maintaining sample integrity, have been carried out in practice. Multiple survey and follow. up teams successfully combined their efforts within the framework of these protocols to detect this planet. This is the second planet in the Spitzer Galactic distribution sample. Both are in the near. to. mid-disk and are clearly not in the Galactic bulge.</P>
<i>SPITZER</i>MICROLENS MEASUREMENT OF A MASSIVE REMNANT IN A WELL-SEPARATED BINARY
Shvartzvald, Y.,Udalski, A.,Gould, A.,Han, C.,Bozza, V.,Friedmann, M.,Hundertmark, M.,Beichman, C.,Bryden, G.,Novati, S. Calchi,Carey, S.,Fausnaugh, M.,Gaudi, B. S.,Henderson, C. B.,Kerr, T.,Pogge, R. IOP Publishing 2015 The Astrophysical journal Vol.814 No.2
<P>We report the detection and mass measurement of a binary lens OGLE-2015-BLG-1285La, b, with the more massive component having M-1 > 1.35M(circle dot) (80% probability). A main-sequence star in this mass range is ruled out by limits on blue light, meaning that a primary in this mass range must be a neutron star (NS) or black hole (BH). The system has a projected separation r(perpendicular to) = 6.1 +/- 0.4 AU and lies in the Galactic bulge. These measurements are based on the 'microlens parallax' effect, i.e., comparing the microlensing light curve as seen from Spitzer, which lay at 1.25 AU projected from Earth, to the light curves from four ground-based surveys, three in the optical and one in the near-infrared. Future adaptive optics imaging of the companion by 30 m class telescopes will yield a much more accurate measurement of the primary mass. This discovery both opens the path and defines the challenges to detecting and characterizing BHs and NSs in wide binaries, with either dark or luminous companions. In particular, we discuss lessons that can be applied to future Spitzer and Kepler K2 microlensing parallax observations.</P>
MOA-2010-BLG-073L: AN M-DWARF WITH A SUBSTELLAR COMPANION AT THE PLANET/BROWN DWARF BOUNDARY
Street, R. A.,Choi, J.-Y.,Tsapras, Y.,Han, C.,Furusawa, K.,Hundertmark, M.,Gould, A.,Sumi, T.,Bond, I. A.,Wouters, D.,Zellem, R.,Udalski, A.,Snodgrass, C.,Horne, K.,Dominik, M.,Browne, P.,Kains, N.,Br IOP Publishing 2013 The Astrophysical journal Vol.763 No.1
<P>We present an analysis of the anomalous microlensing event, MOA-2010-BLG-073, announced by the Microlensing Observations in Astrophysics survey on 2010 March 18. This event was remarkable because the source was previously known to be photometrically variable. Analyzing the pre-event source light curve, we demonstrate that it is an irregular variable over timescales >200 days. Its dereddened color, (V - I)(S),(0), is 1.221 +/- 0.051 mag, and from our lens model we derive a source radius of 14.7 +/- 1.3 R-circle dot, suggesting that it is a red giant star. We initially explored a number of purely microlensing models for the event but found a residual gradient in the data taken prior to and after the event. This is likely to be due to the variability of the source rather than part of the lensing event, so we incorporated a slope parameter in our model in order to derive the true parameters of the lensing system. We find that the lensing system has a mass ratio of q = 0.0654 +/- 0.0006. The Einstein crossing time of the event, t(E) = 44.3 +/- 0.1 days, was sufficiently long that the light curve exhibited parallax effects. In addition, the source trajectory relative to the large caustic structure allowed the orbital motion of the lens system to be detected. Combining the parallax with the Einstein radius, we were able to derive the distance to the lens, D-L = 2.8 +/- 0.4 kpc, and the masses of the lensing objects. The primary of the lens is an M-dwarf with M-L,M-1 = 0.16 +/- 0.03 M-circle dot, while the companion has M-L,M-2 = 11.0 +/- 2.0 M-J, putting it in the boundary zone between planets and brown dwarfs.</P>