Bright-dark mixed NN-soliton solutions of the multi-component Mel'nikov system

By virtue of the KP hierarchy reduction technique, we construct the general bright-dark mixed $N$-soliton solution to the multi-component Mel'nikov system comprised of multiple (say $M$) 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 $N$-soliton solutions in short-wave components of the three-component Mel'nikov system are derived in detail. Then we extend our analysis to the $M$-component Mel'nikov system to obtain its general mixed $N$-soliton solution. The formula obtained unifies the all-bright, all-dark and bright-dark mixed $N$-soliton solutions. For the collision of two solitons, the asymptotic analysis shows that for a $M$-component Mel'nikov system with $M \geq 3$, 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

High-order rogue waves of a long wave-short wave model

The long wave-short wave model describes the interaction between the long wave and the short wave. Exact higher-order rational solution expressed by determinants is calculated via the Hirota's bilinear method and the KP hierarchy reduction. It is found that the fundamental rogue wave for the short wave can be classified into three different patterns: bright, intermediate and dark ones, whereas the rogue wave for the long wave is always bright type. The higher-order rogue waves correspond to the superposition of fundamental rogue waves. The modulation instability analysis show that the condition of the baseband modulation instability where an unstable continuous-wave background corresponds to perturbations with infinitesimally small frequencies, coincides with the condition for the existence of rogue-wave solutions.Comment: 14 pages, 5 figure

Two-component Analogue of Two-dimensional Long Wave-Short Wave Resonance Interaction Equations: A Derivation and Solutions

The two-component analogue of two-dimensional long wave-short wave resonance interaction equations is derived in a physical setting. Wronskian solutions of the integrable two-component analogue of two-dimensional long wave-short wave resonance interaction equations are presented.Comment: 16 pages, 9 figures, revised version; The pdf file including all figures: http://www.math.utpa.edu/kmaruno/yajima.pd

The suppression of short waves by a train of long waves

It is shown that a train of long waves can suppress a short-wave field due to four-wave resonance interactions. These interactions lead to the diffusion (in Fourier space) of the wave action of the short-wave field, so that the wave action is transported to the regions of higher wavenumbers, where it dissipates more effectively. The diffusion equation is derived

Sensitivity of a distributed temperature-radiation index melt model based on AWS observations and surface energy balance fluxes, Hurd Peninsula glaciers, Livingston Island, Antarctica

We use an automatic weather station and surface mass balance dataset spanning four melt seasons collected on Hurd Peninsula Glaciers, South Shetland Islands, to investigate the point surface energy balance, to determine the absolute and relative contribution of the various energy fluxes acting on the glacier surface and to estimate the sensitivity of melt to ambient temperature changes. Long-wave incoming radiation is the main energy source for melt, while short-wave radiation is the most important flux controlling the variation of both seasonal and daily mean surface energy balance. Short-wave and long-wave radiation fluxes do, in general, balance each other, resulting in a high correspondence between daily mean net radiation flux and available melt energy flux. We calibrate a distributed melt model driven by air temperature and an expression for the incoming short-wave radiation. The model is calibrated with the data from one of the melt seasons and validated with the data of the three remaining seasons. The model results deviate at most 140 mm w.e. from the corresponding observations using the glaciological method. The model is very sensitive to changes in ambient temperature: a 0.5 ◦ C increase results in 56 % higher melt rates

Short-Wave Excitations in Non-Local Gross-Pitaevskii Model

It is shown, that a non-local form of the Gross-Pitaevskii equation allows to describe not only the long-wave excitations, but also the short-wave ones in the systems with Bose-condensate. At given parameter values, the excitation spectrum mimics the Landau spectrum of quasi-particle excitations in superfluid Helium with roton minimum. The excitation wavelength, at which the roton minimum exists, is close to the inter-particle interaction range. It is shown, that the existence domain of the spectrum with a roton minimum is reduced, if one accounts for an inter-particle attraction.Comment: 5 pages, 5 figures, UJP style; presented at Bogolyubov Kyiv Conference "Modern Problems of Theoretical and Mathematical Physics", September 15-18, 200