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In this paper, we extend the Petviashvili method (PM) to the fractional nonlinear Schr\"{o}dinger equation (fNLSE) for the construction and analysis of its soliton solutions. We also investigate the temporal dynamics and stabilities of the soliton solutions of the fNLSE by implementing a spectral method, in which the fractional-order spectral derivatives are computed using FFT routines, and the time integration is performed by a $4^{th}$ order Runge-Kutta time-stepping algorithm. We discuss the effects of the order of the fractional derivative, $\alpha$, on the properties, shapes, and temporal dynamics of the solitons solutions of the fNLSE. We also examine the interaction of those soliton solutions with zero, photorefractive and q-deformed Rosen-Morse potentials. We show that for all of these potentials the soliton solutions of the fNLSE exhibit a splitting and spreading behavior, yet their dynamics can be altered by the different forms of the potentials and noise considered., Comment: Typos are corrected and results and discussions are elaborated in v2 of the paper

Long waves bring many important challenges in the ocean and coastal engineering, including but are not limited to harbor resonance and run-up. Therefore, understanding and modeling their dynamics is crucially important. Although their dynamics over various types of geometries are well-studied in the literature, the study of the geometries with power-law variations remains an open problem in this setting. With this motivation, in this paper, we derive the exact analytical solutions of the long-wave equation over nonlinear depth and breadth profiles having power-law forms given by $h(x)=c_1 x^a$ and $b(x)=c_2 x^c$, where the parameters $c_1, c_2, a, c$ are some constants. We show that for these types of power-law forms of depth and breadth profiles, the long-wave equation admits solutions in terms of Bessel functions and Cauchy-Euler series. We also derive the seiching periods and resonance conditions for these forms of depth and breadth variations. Our results can be used to investigate the long-wave dynamics and their envelope characteristics over equilibrium beach profiles, the effects of nonlinear harbor entrances and angled nonlinear seawall breadth variations in the power-law forms on these dynamics, and the effects of reconstruction, geomorphological changes, sedimentation, and dredging to harbor resonance, to the shift in resonance periods and to the seiching characteristics in lakes and barrages., Comment: Typos corrected

Bound entanglement was shown to be activated [P. Horodecki \textit{et al.,} Phys. Rev. Lett. \textbf{82,} 1056 (1999)] in the sense that the entanglement of a spatially separated two-qutrit system can be increased with nonzero probability via a sufficiently large number of preshared bound-entangled states, local three-level controlled operations, and classical communications. Here, we present a local quantum Zeno scheme for activating bound entanglement which is based only on single-particle rotations and threshold measurements. In our scheme, neither a large number of bound-entangled states nor controlled operations are required, and classical communication is required only once at the end of the protocol. We show that a single bound-entangled state is sufficient for increasing the negativity of the target entangled state from 0.11 to 0.17, and by using four more bound-entangled states, negativity can be made greater than 0.42 and the fidelity to the maximally entangled state increases from 0.3 to 0.41, 0.50, 0.59, and 0.61. We believe our results are important not only for quantum technologies but also for a better understanding of quantum entanglement., Comment: 10 pages, 4 figures

In this paper, we discuss the usage and implementation of the compressive sensing (CS) for the efficient measurement and analysis of the von K\'arm\'an vortices. We consider two different flow fields, the flow fields around a circle and an ellipse. We solve the governing $k-\epsilon$ transport equations numerically in order to model the flow fields around these bodies. Using the time series of the drag, $C_D$, and the lift, $C_L$, coefficients, and their Fourier spectra, we show that compressive sampling can be effectively used to measure and analyze Von K\'arm\'an vortices. We discuss the effects of the number of samples on reconstruction and the benefits of using compressive sampling over the classical Shannon sampling in the flow measurement and analysis where Von K\'arm\'an vortices are present. We comment on our findings and indicate their possible usage areas and extensions. Our results can find many important applications including but are not limited to measure, control, and analyze vibrations around coastal and offshore structures, bridges, aerodynamics, and Bose-Einstein condensation, just to name a few.

In this paper, we discuss the usage and implementation of the compressive sensing (CS) for the efficient measurement and analysis of the von K��rm��n vortices. We consider two different flow fields, the flow fields around a circle and an ellipse. We solve the governing $k-��$ transport equations numerically in order to model the flow fields around these bodies. Using the time series of the drag, $C_D$, and the lift, $C_L$, coefficients, and their Fourier spectra, we show that compressive sampling can be effectively used to measure and analyze Von K��rm��n vortices. We discuss the effects of the number of samples on reconstruction and the benefits of using compressive sampling over the classical Shannon sampling in the flow measurement and analysis where Von K��rm��n vortices are present. We comment on our findings and indicate their possible usage areas and extensions. Our results can find many important applications including but are not limited to measure, control, and analyze vibrations around coastal and offshore structures, bridges, aerodynamics, and Bose-Einstein condensation, just to name a few.

In this paper, we propose a numerical framework to study the shapes, dynamics and the stabilities of the self-localized solutions of the nonlinear wave blocking problem. With this motivation, we use the nonlinear Schr\"odinger equation (NLSE) derived by Smith as a model for the nonlinear wave blocking. We propose a spectral renormalization method (SRM) to find the self-localized solitons of this model. We show that for constant, linearly varying or sinusoidal current gradient, i.e. dU/dx, the self-localized solitons of the Smith's NLSE do exist. Additionally, we propose a spectral scheme with 4th order Runge-Kutta time integrator to study the temporal dynamics and stabilities of such solitons. We observe that self-localized solitons are stable for the cases of constant or linearly varying current gradient however, they are unstable for sinusoidal current gradient, at least for the selected parameters. We comment on our findings and discuss the importance and the applicability of the proposed approach., Comment: Typos are corrected

In this paper, we propose the existence and discuss the properties of rogue quantum gravitational waves. More specifically, we numerically solve the Schr\"odinger-Newton system of equations using a spectral scheme with a $4^{th}$ order Runge-Kutta time integrator and show that noise either imposed on wave function $\Psi$, or the gravitational field $\Phi$, triggers the modulation instability which turns the monochromatic wave fields into chaotic ones exhibiting high and unexpected waves. Such waves can be named as rogue quantum gravitational waves. We discuss the characteristics and probabilities of occurrences of such rogue waves in the frame of the Schr\"odinger-Netwon equations. We suggest alternative methods for studying rogue quantum gravitational waves and rogue gravitational waves.

In this paper, we propose and apply a deep learning strategy for the early detection of the Draupner rogue (freak) wave, which is also known as the New Year's wave. We use a long short term memory (LSTM) network and show that Draupner rogue wave could have been observed at least minutes before the catastrophically dangerous peak has appeared in the chaotic wave field using the available data. Compared to the existing early warning times scales on the order of seconds, this is a major step forward which will certainly enhance the safety and understanding of the marine engineering. As the rogue wave data sets get improved in the future, our results may be enhanced to increase the early warning time scales. Our results can be used to predict other rogue waves and extreme time-series phenomena in fields including but are not limited to hydrodynamics and marine engineering, optics, finance, and Bose-Einstein condensation, just to name a few.

In this paper we numerically analyze the 1D self-localized solutions of the Kundu-Eckhaus equation (KEE) in nonlinear waveguides using the spectral renormalization method (SRM) and compare our findings with those solutions of the nonlinear Schrodinger equation (NLSE). We show that single, dual and N-soliton solutions exist for the case with zero optical potentials, i.e. V=0. We also show that these soliton solutions do not exist, at least for a range of parameters, for the photorefractive lattices with optical potentials in the form of V=Io cos^2(x) for cubic nonlinearity. However, self-stable solutions of the KEE with saturable nonlinearity do exist for some range of parameters. We compare our findings for the KEE with those of the NLSE and discuss our results., Typos are corrected, 8 figures are added

In this paper we discuss the possible usage of the compressive sampling based wavelet analysis for the efficient measurement and for the early detection of one dimensional (1D) vibrational rogue waves. We study the construction of the triangular (V-shaped) wavelet spectra using compressive samples of rogue waves that can be modeled as Peregrine and Akhmediev-Peregrine solitons. We show that triangular wavelet spectra can be sensed by compressive measurements at the early stages of the development of vibrational rogue waves. Our results may lead to development of the efficient vibrational rogue wave measurement and early sensing systems with reduced memory requirements which use the compressive sampling algorithms. In typical solid mechanics applications, compressed measurements can be acquired by randomly positioning single sensor and multisensors.

In this paper we propose an efficient tomographic approach for the early detection of 2D rogue waves. The method relies on the principle of detecting conical spectral features before rogue wave becomes evident in time. More specifically, the proposed method is based on constructing the 1D Radon transforms of the emerging conical 2D spectra of the wavefield using compressive sampling (CS) and then constructing 2D spectra from those projections using filtered back projection (FBP) algorithm. For the 2D rogue wave models we use the radially symmetric Peregrine soliton and Akhmediev-Peregrine soliton solutions of the nonlinear Schrodinger equation, which can model characteristics of the peaked structure of 2D rogue waves and their conical spectra which may be treated as a sparse signal. We show that emerging conical spectra of 2D rogue waves before they become evident in time can be acquired efficiently by the proposed method.

In this paper, we study the effects of white-noised potentials on nonlinear quantum tunneling. We use a split-step scheme to numerically solve the nonlinear Schrodinger equation (NLSE) with a tunneling potential. We consider three different types of potentials, namely; the single rectangular barrier, double rectangular barrier, and triangular barrier. For all these three cases, we show that white-noise given to potentials do not trigger modulation instability for tunneling of the sech type soliton solutions of the NLSE. However, white-noised potentials trigger modulation instability for tunneling of the sinusoidal wavefunctions; thus, such a wavefield turns into a chaotic one with many apparent peaks. We argue that peaks of such a field may be in the form of rational rogue wave solutions of the NLSE. Our results can be used to examine the effects of noise on quantum tunneling. Since a rogue wavefunction means a higher probability of the tunneling particle to be at a given (x,t) coordinate, our results may also be used for developing the quantum science and technology with many possible applications including but are not limited to increasing the resolution and efficiency of scanning tunneling microscopes, enhancing proton tunneling for DNA mutation and enhancing superconducting properties of junctions. Publisher's Version

In this paper we propose an extended Kundu-Eckhaus equation (KEE) for modeling the dynamics of skewed rogue waves emerging in the vicinity of a wave blocking point due to opposing current. The equation we propose is a KEE with an additional potential term therefore the results presented in this paper can easily be generalized to study the quantum tunneling properties of the rogue waves and ultrashort (femtosecond) pulses of the KEE. In the frame of the extended KEE, we numerically show that the chaotic perturbations of the ocean current trigger the occurrence of the rogue waves on the ocean surface. We propose and implement a split-step scheme and show that the extended KEE that we propose is unstable against random chaotic perturbations in the current profile. These perturbations transform the monochromatic wave field into a chaotic sea state with many peaks. We numerically show that the shapes of rogue waves due to perturbations in the current profile closely follow the form of rational rogue wave solutions, especially for the central peak. We also discuss the effects of magnitude of the chaotic current perturbations on the statistics of the rogue wave occurrence., Typos are added

In this study the detection of the oil spill using synthetic aperture radar (SAR) imagery is considered. Detection of the oil spill is performed using change detection algorithms between imagery acquired at different times. The specific algorithms used are the correlation coefficient change statistic and the intensity ratio change statistic algorithms. Therefore these algorithms and the probabilistic selection of the threshold criteria is reviewed and discussed. A recently offered change detection method which depends on the idea of generating two different final change maps of two images in a sequence, is used. First final change map is obtained by cumulatively adding the sequences of change maps in such a manner that common change areas are excluded and uncommon change areas are included. The second final change map is obtained by comparing the first and the last images in the temporal sequence. This method requires at least three images to be employed and can be generalized to longer temporal image sequences. The purpose of this approach is to provide a double check mechanism to the conventional approach and thus to reduce the probability of false alarm and enhance the change detection. The algorithms mentioned are applied to a 2010 Gulf of Mexico oil spill imagery together with the method described. It is shown that intensity ratio change statistic is a better tool for identification of the changes due to the oil spill compared to the correlation coefficient change statistic. It is also shown that two final change map method can reduce the probability of false alarm. The data used in this study is acquired by the Japanese Aerospace Agency's Advanced Land Observing Satellite (ALOS) through Alaska SAR Facility (ASF) at the University of Alaska, Fairbanks, AK.

We discuss the possible usage of the compressive sampling for the early detection of rogue waves. One of the promising techniques for the early detection of the oceanic rogue waves is to measure the triangular Fourier spectra which begin to appear at the early stages of their development. For the early detection of the rogue waves it is possible to treat such a spectrum as a sparse signal since we would mainly be interested in the high amplitude triangular region located at the central wavenumber. Therefore compressive sampling can be a very efficient tool for the rogue wave early warning systems. Compressed measurements can be acquired by remote sensing techniques such as coherent SAR which measure the ocean surface envelope or by insitu techniques such as spectra measuring tools mounted on a ship hull or bottom mounted pressure gauges. By employing a numerical approach we show that triangular Fourier spectra can be sensed by compressive measurements at the early stages of the development of rogue waves such as those in the form of Peregrine and Akhmediev-Peregrine solitons. Our results may lead to development of the early warning hardware systems which use the compressive sampling thus the memory requirements for those systems can be greatly reduced., Comment: arXiv admin note: text overlap with arXiv:1512.02583

The idea of ocean and sea wave energy conversion has started spreading in the early 1800s. By the 1973 the patents issued in this area has reached the 340 with many different designs. Today there exist many designs which relies on many principles such as using waves, tides, currents, temperature difference, biological and nuclear components. In this study a translation of a paper has been published in 1911 in Şehbal journal for introducing two wave energy conversion systems is presented aiming to shed light on Ottoman science history studies., Okyanus ve deniz dalgalarından enerji üretme fikri 1800’lerin başlarında yaygınlaşmaya başlamıştır. 1973’e gelindiğinde ise bu konuda alınan patent sayısı çok sayıda değişik tasarımla 340’a ulaşmıştır. Günümüzde ise dalga, gelgit, akıntı, sıcaklık farkı, biyolojik ve nükleer bileşenleri kullanma gibi birçok ilkeye dayanan tasarımlar mevcuttur. Bu çalışmada 1911 yılında Şehbal dergisinde dalgalardan enerji üreten iki sistemi tanıtmak için yayınlanan bir yazının çevirisi Osmanlı bilim tarihi araştırmalarına ışık tutması amacıyla sunulmuştur.

In this paper an approach for decreasing the computational effort required for the spectral simulations of the water waves is introduced. Signals with majority of the components zero, are known as the sparse signals. Like majority of the signals in the nature it can be realized that water waves are sparse either in time or in the frequency domain. Using the sparsity property of the water waves in the time or in the frequency domain, the compressive sampling algorithm can be used as a tool for improving the performance of the spectral simulation of the water waves. The methodology offered in this paper depends on the idea of using a smaller number of spectral components compared to the classical spectral method with a high number of components. After performing the time integration with a smaller number of spectral components and using the compressive sampling technique, it is shown that the water wave field can be reconstructed with a significantly better efficiency compared to the classical spectral method with a high number of spectral components, especially for long time evolutions. For the sparse water wave model in the time domain the well-known solitary wave solutions of the Korteweg-deVries (KdV) equation is considered. For the sparse water wave model in the frequency domain the well-known Airy (linear) ocean waves with Jonswap spectrum is considered. Utilizing a spectral method, it is shown that by using a smaller number of spectral components compared to the classical spectral method with a high number of components, it is possible to simulate the sparse water waves with negligible error in accuracy and a great efficiency especially for large time evolutions., Comment: arXiv admin note: text overlap with arXiv:1512.03932