Rogue wave modes for the coupled nonlinear Schrodinger system with three components: A computational study

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A system of coupled partial differential equations exhibiting both elevation and depression rogue wave modes

Analytical solutions are obtained for a coupled system of partial differential equations involving hyperbolic differential operators. Oscillatory states are calculated by the Hirota bilinear transformation. Algebraically localized modes are derived by taking a Taylor expansion. Physically these equations will model the dynamics of water waves, where the dependent variable (typically the displacement of the free surface) can exhibit a sudden deviation from an otherwise tranquil background. Such modes are termed ‘rogue waves’ and are associated with ‘extreme and rare events in physics’. Furthermore, elevations, depressions and ‘four-petal’ rogue waves can all be obtained by modifying the input parameters.postprin

Breathers and 'black' rogue waves of coupled nonlinear Schrödinger equations with dispersion and nonlinearity of opposite signs

Breathers and rogue waves of special coupled nonlinear Schrödinger systems (the Manakov equations) are studied analytically. These systems model the orthogonal polarization modes in an optical fiber with randomly varying birefringence. Studies earlier in the literature had shown that rogue waves can occur in these Manakov systems with dispersion and nonlinearity of opposite signs, and that the criterion for the existence of rogue waves correlates closely with the onset of modulation instability. In the present work the Hirota bilinear transform is employed to calculate the breathers (pulsating modes), and rogue waves are obtained as a long wave limit of such breathers. In terms of wave profiles, a ‘black’ rogue wave (intensity dropping to zero) and the transition to a four-petal configuration are elucidated analytically. Sufficiently strong modulation instabilities of the background may overwhelm or mask the development of the rogue waves, and such thresholds are correlated to actual physical properties of optical fibers. Numerical simulations on the evolution of breathers are performed to verify the prediction of the analytical formulations.postprin

A coupled 'AB' system: Rogue waves and modulation instabilities

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Rogue wave modes for a derivative nonlinear Schrödinger model

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The effects of stent porosity on the endovascular treatment of intracranial aneurysms located near a bifurcation

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β\beta-Stars or On Extending a Drawing of a Connected Subgraph

We consider the problem of extending the drawing of a subgraph of a given plane graph to a drawing of the entire graph using straight-line and polyline edges. We define the notion of star complexity of a polygon and show that a drawing $\Gamma_H$ of an induced connected subgraph $H$ can be extended with at most $\min\{ h/2, \beta + \log_2(h) + 1\}$ bends per edge, where $\beta$ is the largest star complexity of a face of $\Gamma_H$ and $h$ is the size of the largest face of $H$. This result significantly improves the previously known upper bound of $72|V(H)|$ [5] for the case where $H$ is connected. We also show that our bound is worst case optimal up to a small additive constant. Additionally, we provide an indication of complexity of the problem of testing whether a star-shaped inner face can be extended to a straight-line drawing of the graph; this is in contrast to the fact that the same problem is solvable in linear time for the case of star-shaped outer face [9] and convex inner face [13].Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018

Rogue wave modes for the long wave-short wave resonance model

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Biodiversity and Biogeography of Chthamalid Barnacles from the North-Eastern Pacific (Crustacea Cirripedia)

The biogeography and ecology of the species of Chthamalus present on the west coast of America are described, using data from 51 localities from Alaska to Panama, together with their zonation on the shore with respect to that of other barnacles. The species present were C. dalli, Pilsbry 1916, C. fissus, Darwin, 1854, C. anisopoma Pilsbry 1916 and four species in the C. panamensis complex. The latter are C. panamensis Pilsbry, 1916, C. hedgecocki, Pitombo & Burton, 2007, C. alani nom. nov. (formerly C. southwardorum Pitombo & Burton, 2007) and C. newmani sp. nov.). These four species were initially separated by enzyme electrophoresis. They could only be partially separated by DNA bar coding but may be separated using morphological characters