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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]

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]

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]

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]