Solitary wave solutions for a generalized KdV–mKdV equation with variable coefficients

In this work, a generalized time-dependent variable coefficients combined KdV–mKdV (Gardner) equation arising in plasma physics and ocean dynamics is studied. By means of three amplitude ansatz that possess modified forms to those proposed by Wazwaz in 2007, we have obtained the bell type solitary waves, kink type solitary waves, and combined type solitary waves solutions for the considered model. Importantly, the results show that there exist combined solitary wave solutions in inhomogeneous KdV-typed systems, after proving their existence in the nonlinear Schrödinger systems. It should be noted that, the characteristics of the obtained solitary wave solutions have been expressed in terms of the time-dependent coefficients. Moreover, we give the formation conditions of the obtained solutions for the considered KdV–mKdV equation with variable coefficients.     

Periodic and solitary wave solutions of the attractive and repulsive nonlinear Schrödinger equation

By means of symbolic computation, the first integral method is presented to obtain novel exact solutions of the nonlinear evolution equation. The obtained results include periodic and solitary wave solutions. The power of this manageable method is confirmed and the availability of symbolic computation is demonstrated.     

Exact wave solutions for a (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation

In this work, we investigate a (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation. Based on the simplified Hirota bilinear method, we first construct its soliton solutions. Meanwhile, we correct the formula of N-soliton solution for this equation. On the basis of these solitons we further calculate its lump solutions, periodic waves. Meanwhile, rogue waves as well as interaction solutions of this equation are also obtained by a direct algebraic method. Some figures are given to display the behavior of these solutions.     

Solitary wave solutions of (3+1)-dimensional extended Zakharov–Kuznetsov equation by Lie symmetry approach

In this paper, the solitary wave solutions of (3+1)-dimensional extended Zakharov–Kuznetsov (eZK) equation are constructed which appear in the magnetized two-ion-temperature dusty plasma and quantum physics. Lie group of transformation method is proposed to investigate the solution of (3+1)-dimensional eZK equation via Lie symmetry method. The optimal system of one dimensional Lie subalgebra is constructed by using Lie point symmetries. The three dimensional eZK equation reduced into number of ordinary differential equations (ODEs) by applying similarity reductions. Consequently, solutions so extracted are more general than erstwhile known results. We have obtained twenty one solutions in the explicit form, some of them are likewise general and some are new for the best study of us. Eventually, single soliton, quasi-periodic soliton, multisoliton, lump-type soliton, traveling wave and solitary wave-interaction behavior are illustrated graphically through numerical simulation for physical affirmation of the results. Please check whether the affiliations are correct.     

Bifurcation and exact traveling wave solutions for dual power Zakharov–Kuznetsov–Burgers equation with fractional temporal evolution

In this article, we introduce the dual power Zakharov–Kuznetsov–Burgers equation with fractional temporal evolution in the sense of modified Riemann–Liouville derivative. We investigate the dynamical behavior, bifurcations and phase portrait analysis of the exact traveling wave solutions of the system with and without damping effect. We apply the $(G^{\prime }∕G)$-expansion method in context of fractional complex transformation and seek a variety of exact traveling wave solutions including solitary wave, kink-type wave, breaking wave and periodic wave solutions of the equation. Furthermore, the remarkable features of the traveling wave solutions and phase portraits of dynamical system are demonstrated through interesting figures.     

Jacobi elliptic wave solutions for two variable coefficients cylindrical Korteweg–de Vries models arising in dusty plasmas by using direct reduction method

In this paper, generalized models for both ($2+1$)-dimensional cylindrical modified Korteweg–de Vries (cmKdV) equation with variable coefficients and ($3+1$)-dimensional variable coefficients cylindrical Korteweg–de Vries (cKdV) equation are studied by direct reduction method. A direct reduction to nonlinear ordinary differential equations in the form of Riccati equations obtained for the considered equations under some integrability conditions. The search for solutions for the reduced Riccati equations has yielded many Jacobi elliptic wave solutions, solitary and periodic wave solutions for both ($2+1$)-dimensional cmKdV and ($3+1$)-dimensional cKdV equations. Physical application for the obtained solutions as dust ion acoustic waves in plasma physics is given     

Applicability of SAR-based wave retrieval for wind–wave interaction analysis in the fetch-limited Baltic

In this article, a method for the detection of wave field parameters from synthetic aperture radar (SAR) imagery in the fetch-limited Baltic Sea is presented. Over the Baltic Sea region, common southwest (SW) and west (W) winds induce steep waves with shorter wavelengths compared with ocean waves. Thus, with the use of previous SAR sensors (e.g. ENVISAT/ASAR), it was not possible to detect individual waves and retrieve image wave number spectra. Since the year 2007, when TerraSAR-X (TS-X) reached its orbit, high spatial resolution data is available for measuring the sea-state parameters: the individual waves up to 30 m wavelength and their refraction can be distinguished. The main objective of this work was to demonstrate the capability of detecting wave field parameter from (TS-X) imagery in the Baltic Sea. The wave field parameters obtained from the SAR imagery were compared with in situ measurements and the Simulating WAves Nearshore (SWAN) wave model. The comparison of SAR-based wave field information with buoy measurements showed high agreement in case of wave propagation direction (r = 0.95) and wavelength (r = 0.83). A significant correlation is also seen between SWAN- and SAR-derived wave propagation direction (r = 0.87) and wavelengths (r = 0.91). With the case studies, it is shown that SAR data enables one to detect land shadow effects and small-scale wave field variations in the coastal zone. It was shown that SAR data is also valuable for improving and interpreting the wave model results. In consequence of common slanting fetch cases over the Baltic Sea region, it was demonstrated that the peak wave directions differ from the mean wind directions up to 43°.     

基于Authorware的wave音频播放器的设计

介绍了如何使用Authorware开发一个播放wave音频文件的播放器。通过这一设计,意在抛砖引玉,帮助大家在多媒体软件开发中,提高对包括声音在内的多媒体信息的处理能力和软件交互性的设计能力。     

Membrane solutions to Hořava gravity

We have investigated purely gravitational membrane solutions to the Ho?ava nonrelativistic theory of gravity with detailed balance in 3 + 1 dimensions. We find that for arbitrary values of the running parameter λ > 1/3 there exist two branches of membrane solutions, and that in the special case λ = 1 one of them is degenerate, the lapse function being undetermined. For negative values of the cosmological constant, the solution contains a single membrane sitting at the center of space, which extends infinitely in the transverse direction, approaching a Lifshitz metric. For positive values of the cosmological constant, the solution represents a space that is bounded in the transverse direction, with two parallelmembrane-like or point-like singularities sitting at each of the boundaries.     

Locally distributed control of wave equations with variable coefficients

For wave equations with variable coefficients on regions which are not necessarily smooth, we obtain a sufficient condition for the subregion on which the application of control will yield the exact controllability property by using piecewise multiplier method and Riemannian geometry method. Some examples are presented.     

Liouvillian solutions of linear difference–differential equations

For a field k$k$ with an automorphism σ$\sigma$ and a derivation δ$\delta$, we introduce the notion of Liouvillian solutions of linear difference–differential systems {σ(Y)=AY,δ(Y)=BY}$\{\sigma \left(Y\right)=AY,\delta \left(Y\right)=BY\}$ over k$k$ and characterize the existence of Liouvillian solutions in terms of the Galois group of the systems. In the forthcoming paper, we will propose an algorithm for deciding if linear difference–differential systems of prime order have Liouvillian solutions.     

基于Shock wave Flash控件实现Delphi与Flash交互

随着计算机的普及,客户对软件界面的要求越来越高,基于Delphi、VC的界面控件尽管非常丰富,但是若让Flash作为显示界面,会给软件带来更好的效果。以Delphi 2007和Flash CS3为例,探讨如何使Flash和Delphi之间进行完美融合。     

Painlevé analysis,soliton solutions and lump-type solutions of the (3+1)-dimensional generalized KP equation

The Painlevé analysis is applied and the multi-soliton criterion is presented to test the integrability of the (3+1)-dimensional generalized KP equation derived from a Hirota bilinear equation. It is shown that the considered equation does not pass the well known Painlevé test and it is only integrable in a conditional sense. Solitary wave solutions are shown to interact each other like solitons in multiple wave collisions unless some additional conditions are imposed. Moreover, we analyze a class of analytical rational lump-type solutions in detail, which are generated from positive quadratic polynomial function and rationally localized in many directions in the space, based upon the Hirota bilinear form.     

Collaborative applications over peer-to-peer systems–challenges and solutions

Emerging collaborative Peer-to-Peer (P2P) systems require discovery and utilization of diverse, multi-attribute, distributed, and dynamic groups of resources to achieve greater tasks beyond conventional file and processor cycle sharing. Collaborations involving application specific resources and dynamic quality of service goals are stressing current P2P architectures. Salient features and desirable characteristics of collaborative P2P systems are highlighted. Resource advertising, selecting, matching, and binding, the critical phases in these systems, and their associated challenges are reviewed using examples from distributed collaborative adaptive sensing systems, cloud computing, and mobile social networks. State-of-the-art resource discovery/aggregation solutions are compared with respect to their architecture, lookup overhead, load balancing, etc., to determine their ability to meet the goals and challenges of each critical phase. Incentives, trust, privacy, and security issues are also discussed, as they will ultimately determine the success of a collaborative P2P system. Open issues and research opportunities that are essential to achieve the true potential of collaborative P2P systems are discussed.     

Sudden bed changes and wave–current interactions in coastal regions

Mean bottom evolutions due to currents and wind waves, even due to wave–current interactions, are easily computed by averaging mean quantities over one or more wave cycles. However, dealing with fine processes, like breaking waves and bar formations in coastal regions, great quantities of sediment are transported and, as a consequence, considerable erosion and deposition can occur quite rapidly. Other phenomena normally associated with earthquakes, like volcanic eruptions, landslides, etc. occur frequently in various coastal regions of the terrestrial globe. Those problems can only be tackled by using a more complete set of equations with improved wave dispersion characteristics, and taking into account time–bed-level changes. Other characteristic non-linearity phenomena in shallow water regions and wave–current interaction become important factors that have to be considered. From the sedimentary point of view, particularly in terms of the wave and current fields, it is not known whether the existing sand transport models are generally valid.The applicability of a computational structure, based on extended Boussinesq-type equations, and two existing sediment transport models are discussed and confirmed through published data. Numerical results obtained at Ria Formosa, Algarve, in the ambit of the European Union INDIA Project are shown.     

Population-based microbial computing: a third wave of synthetic biology?

Synthetic biology is an emerging research field, in which engineering principles are applied to natural, living systems. A major goal of synthetic biology is to harness the inherent “biological nanotechnology” of living cells for the purposes of computation, production or diagnosis. As the field evolves, it is gradually developing from a single-cell approach (akin to using standalone computers) to a distributed, population-based approach (akin to using networks of connected machines). We anticipate this eventually representing the “third wave” of synthetic biology (the first two waves being the emergence of modules and systems, respectively, with the second wave still yet to peak). In this paper, we review the developments that are leading to this third wave, and describe some of the existing scientific and technological challenges.     

Solving metamaterial Maxwell’s equations via a vector wave integro-differential equation

In this paper, we discuss the time-domain metamaterial Maxwell’s equations. One major contribution of this paper is that after some effort we find that the metamaterial Maxwell’s equations can be beautifully reduced to a vector wave integro-differential equation involving just one unknown, which is quite similar to that obtained from the standard Maxwell’s equations in vacuum. Then we study the existence and uniqueness of this new modeling equations, and propose a fully-discrete finite element method to solve this model. Numerical results justifying our analysis are presented. This discovery shall make simulation of metamaterials much more efficient than the previous works.