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This article concerns an approximate solution for the Benjamin-Bona-Mahony (BBM) equation with a bilinear control in slowly varying medium. By a sharp estimation of the error term, a suitable approximate solution for this equation is established. [ABSTRACT FROM AUTHOR]

We study the inelastic collision of two solitary waves of different velocities for the generalized Benjamin-Bona-Mahony (BBM) equation with cubic nonlinearity. It shows that one solitary wave is smaller than the other one in the H¹ (ℝ) energy space. We explore the sharp estimates of the nonzero residue due to the collision, and prove the inelastic collision of two solitary waves and nonexistence of a pure 2-soliton solution. [ABSTRACT FROM AUTHOR]

We study the initial boundary value problem of the general three-component Camassa-Holm shallow water system on an interval subject to inhomogeneous boundary conditions. First we prove a local in time existence theorem and present a weak-strong uniqueness result. Then, we establish a asymptotic stabilization of this system by a boundary feedback. Finally, we obtain a result of blow-up solution with certain initial data and boundary profiles. [ABSTRACT FROM AUTHOR]

This paper studies the wave-breaking criterion for the generalized weakly dissipative two-component Hunter-Saxton system in the periodic setting. We get local well-posedness for the generalized weakly dissipative two-component Hunter-Saxton system. We study a wave-breaking criterion for solutions and results of wave-breaking solutions with certain initial profiles. [ABSTRACT FROM AUTHOR]

This paper studies the adaptive control problem of the Korteweg-de Vries-Burgers equation. Using the Lyapunov function method, we prove that the closed-loop system including the parameter estimator as a dynamic component is globally L2 stable. Furthermore, we show that the state of the system is regulated to zero by developing an alternative to Barbalat's lemma which cannot be used in the present situation. The closed-loop system is shown to be well posed. [ABSTRACT FROM AUTHOR]

We employ the bifurcation method of planar dynamical systems and qualitative theory of polynomial differential systems to derive new bounded traveling-wave solutions for a variant of the K(3, 2) equation. For the focusing branch, we obtain hump-shaped and valley-shaped solitary wave solutions and some periodic solutions. For the defocusing branch, the nonexistence of solitary traveling wave solutions is shown. Meanwhile, some periodic solutions are also obtained. The results presented in this paper supplement the previous results. [ABSTRACT FROM AUTHOR]

We apply the theory of Weierstrass elliptic function to study exact solutions of the generalized Benjamin-Bona-Mahony equation. By using the theory of Weierstrass elliptic integration, we get some traveling wave solutions, which are expressed by the hyperbolic functions and trigonometric functions. This method is effective to find exact solutions of many other similar equations which have arbitrary-order nonlinearity. [ABSTRACT FROM AUTHOR]

In the paper what is studied is the wild solution of the induced form under the spline wavelet basis in weakly damped forced KdV equation. [ABSTRACT FROM AUTHOR]

The dynamics of the nonlinear Schördinger equation with Kerr law nonlinearity with two perturbation terms are investigated. By Using Melnikov method, the threshold values of chaotic motion under periodic perturbation are given .Moreover we also study the effects of the parameters of system on dynamical behaviors by using numerical simulation. The numerical simulations, including bifurcation diagram of fixed points, chaos threshold diagram of system in three-dimensional space, maximum Lyapunov exponent, and phase portraits, are also plotted to illustrate theoretical analysis and to expose the complex dynamical behaviors. In particular, we observe that the system can leave chaotic region to periodic motion by adjusting controller e, amplitude d 1, and frequency ω2of external forcing which can be considered a control strategy, and when the frequencies y ω2 and ω1 approach the maximum frequency of disturbance, the system turmoil intensifies and control intensity increases. [ABSTRACT FROM AUTHOR]

In underwater acoustic sensor networks (UASNs), the propagation delay of acoustic signals is much longer than Radio Frequency (RF). There is spatial unfairness problem caused by space-time uncertainty. Hence, the design of Medium Access Control (MAC) is a challenging issue. In underwater, it not only considers transmission time but also takes location into account. In this paper, we propose Response to the Earliest Transmitter of RTS MAC (RET-MAC) protocol to solve the problem. RET-MAC adopts adaptive RTS Contention Phase (RTS CP) to determine the earliest transmitter of RTS. And CTS Delay Phase (CTS DP) is added to postpone sending CTS in order to avoid collision. In addition, we propose CTS back-off mechanism to adjust the length of CTS DP as needed. Contention back-off mechanism is used to reduce network congestion and increase fairness further. The simulation results show that our scheme can achieve higher fairness and throughput; at the same time it also guarantees lower energy consumption and delay. [ABSTRACT FROM AUTHOR]

Although detecting and characterizing community structure is key in the study of networked systems, we still do not understand how community structure affects systemic resilience and stability. We use percolation theory to develop a framework for studying the resilience of networks with a community structure. We find both analytically and numerically that interlinks (the connections among communities) affect the percolation phase transition in a way similar to an external field in a ferromagnetic-paramagnetic spin system. We also study universality class by defining the analogous critical exponents δ and γ, and we find that their values in various models and in real-world coauthor networks follow the fundamental scaling relations found in physical phase transitions. The methodology and results presented here facilitate the study of network resilience and also provide a way to understand phase transitions under external fields. [ABSTRACT FROM AUTHOR]

As a developing country, extensive carbon and sulfur emissions are associated with China’s rapid social and economic development. Chief among them are the emissions from coal and oil consumption. This paper focuses on the demand side, attempting to regulate the range of relative price of oil to coal at the consumption level. Through the adjustment of the relative price, the goal of reducing the emissions of carbon and sulfur could be achieved in the market of energy consumption. Data regression is applied to investigate the functional relationship between emissions and energy prices. The results indicate that when the coal price is less than 300, the higher relative price leads to less carbon and sulfur emissions; when the coal price is more than 300 and less than 500, there exists an optimal relative price which has the least carbon emissions, and this value is not more than 11.5; when the coal price is more than 500, the smaller relative price is beneficial to decline carbon and sulfur emissions. The changed trend of relative price-sulfur emissions is very similar to relative price-carbon emissions. Compared to the present energy situation in China, the relative price of oil to coal still need to be reduced especially when coal price is more than 500. [ABSTRACT FROM AUTHOR]

We report a new method for growing hexagonal columnar nanograin structured silicon carbide (SiC) thin films on silicon substrates by using graphene-graphitic carbon nanoflakes (GGNs) templates from solid carbon sources. The growth was carried out in a conventional low pressure chemical vapor deposition system (LPCVD). The GGNs are small plates with lateral sizes of around 100 nm and overlap each other, and are made up of nanosized multilayer graphene and graphitic carbon matrix (GCM). Long and straight SiC nanograins with hexagonal shapes, and with lateral sizes of around 200-400 nm are synthesized on the GGNs, which form compact SiC thin films. [ABSTRACT FROM AUTHOR]

Network systems with clustering have been given much attention due to their wide occurrence in the real world. One focus of these studies has been on robustness of single clustered networks and interdependent clustered networks under random attack (RA) or hub-targeted attack. However, infrastructure networks could suffer from a damage that is localized, i.e. a group of neighboring nodes attacked or fail, a topic that was not studied earlier on clustered networks. In this paper, we analytically and via simulations study the robustness under localized attack (LA) of single Erdős–Rényi clustered network and interdependent clustered network. For generating networks with clustering we use two models: (i) double Poisson distribution (DPD) and (ii) fixed degree distribution (FDD). For the LA case, the DPD model shows a second order phase transition behavior for a single clustered network, while for dependent networks, the system undergoes a change of percolation phase transition from a first order (abrupt transition) to a second order (continuous) transition when the coupling strength q decreases below a critical value qc. Our results imply that single networks become significantly more vulnerable with increasing clustering coefficient c with respect to LA. This is in contrast to RA where the robustness is almost independent of c. We obtain similar results when testing different real networks. For LA on dependent networks, we also observe that the system becomes more vulnerable as c increases. This is again in contrast to RA, where for, q < qc, the system robustness is almost unaffected by increasing clustering. We also solved analytically the case of LA on random regular networks which are clustered and interdependent and find that as m (the number of clustered networks that each network depends on) or c increases, the system becomes significantly more vulnerable. We also analyzed via simulations the case of generating clustering in networks for the model of keeping a FDD, and find that the influence of clustering on the robustness of two partially interdependent networks under LA is smaller than for DPD, which is very different from these cases under RA. [ABSTRACT FROM AUTHOR]