Chinese Physics B

Zhaqilao,

doi: 10.1088/1674-1056/22/4/040201pmid: N/A

In this paper, we studied N-soliton solutions of a new integrable equation studied by Qiao [J. Math. Phys. 48 082701 (2007)]. Firstly, we employed the Darboux matrix method to construct a Darboux transformation for the modified Korteweg-de Vries equation. Then we use the Darboux transformation and a transformation, introduced by Sakovich [J. Math. Phys. 52 023509 (2011)], to derive N-soliton solutions of the new integrable equation from the seed solution. In particular, the multiple soliton solutions are explicitly obtained and shown through some figures.

Lei, Ya; Yang, Duo

doi: 10.1088/1674-1056/22/4/040202pmid: N/A

In this paper, the finite symmetry transformation group of the (2+1)-dimensional coupled Burgers equation is studied by the modified direct method, and with the help of the truncated Painlevé expansion approach, some special localized structures for the (2+1)-dimensional coupled Burgers equation are obtained, in particular, the dromion-like and solitoff-like structures.

Ji, Liang-Hao; Liao, Xiao-Feng

doi: 10.1088/1674-1056/22/4/040203pmid: N/A

Consensus problems of first-order multi-agent systems with multiple time delays are investigated in this paper. We discuss three cases: 1) continuous, 2) discrete, and 3) a continuous system with a proportional plus derivative controller. In each case, the system contains simultaneous communication and input time delays. Supposing a dynamic multi-agent system with directed topology that contains a globally reachable node, the sufficient convergence condition of the system is discussed with respect to each of the three cases based on the generalized Nyquist criterion and the frequency-domain analysis approach, yielding conclusions that are either less conservative than or agree with previously published results. We know that the convergence condition of the system depends mainly on each agent's input time delay and the adjacent weights but is independent of the communication delay between agents, whether the system is continuous or discrete. Finally, simulation examples are given to verify the theoretical analysis.

Gong, Yong-Wang; Song, Yu-Rong; Jiang, Guo-Ping

doi: 10.1088/1674-1056/22/4/040204pmid: N/A

In this paper, we study worm dynamics in computer networks composed of many autonomous systems. A novel multi-group SIQR (susceptible-infected-quarantined-removed) model is proposed for computer worms by explicitly considering anti-virus measures and the network infrastructure. Then, the basic reproduction number of worm R0 is derived and the global dynamics of the model are established. It is shown that if R0 is less than or equal to 1, the disease-free equilibrium is globally asymptotically stable and the worm dies out eventually, whereas, if R0 is greater than 1, one unique endemic equilibrium exists and it is globally asymptotically stable, thus the worm persists in the network. Finally, numerical simulations are given to illustrate the theoretical results.

Song, Yu-Rong; Jiang, Guo-Ping; Gong, Yong-Wang

doi: 10.1088/1674-1056/22/4/040205pmid: N/A

In the propagation of an epidemic in a population, individuals adaptively adjust their behavior to avoid the risk of an epidemic. Differently from existing studies where new links are established randomly, a local link is established preferentially in this paper. We propose a new preferentially reconnecting edge strategy depending on spatial distance (PR-SD). For the PR-SD strategy, the new link is established at random with probability p and in a shortest distance with the probability 1 p. We establish the epidemic model on an adaptive network using Cellular Automata, and demonstrate the effectiveness of the proposed model by numerical simulations. The results show that the smaller the value of parameter p, the more difficult the epidemic spread is. The PR-SD strategy breaks long-range links and establishes as many short-range links as possible, which causes the network efficiency to decrease quickly and the propagation of the epidemic is restrained effectively.

Wang, Ya-Qi; Yang, Xiao-Yuan

doi: 10.1088/1674-1056/22/4/040206pmid: N/A

In this paper, an extended version of standard susceptible-infected (SI) model is proposed to consider the influence of a medium access control mechanism on virus spreading in wireless sensor networks. Theoretical analysis shows that the medium access control mechanism obviously reduces the density of infected nodes in the networks, which has been ignored in previous studies. It is also found that by increasing the network node density or node communication radius greatly increases the number of infected nodes. The theoretical results are confirmed by numerical simulations.

Da, .; Irk, D.; Sar, M.

doi: 10.1088/1674-1056/22/4/040207pmid: N/A

A collocation method based on an extended cubic B-spline function is introduced for the numerical solution of the modified regularized long wave equation. The accuracy of the method is illustrated by studying the single solitary wave propagation and the interaction of two solitary waves of the modified regularized long wave equation.

Hamzavi, M.; Ikhdair, S. M.; Thylwe, K. E.

doi: 10.1088/1674-1056/22/4/040301pmid: N/A

We present analytical bound state solutions of the spin-zero KleinGordon (KG) particles in the field of unequal mixture of scalar and vector Yukawa potentials within the framework of the approximation scheme to the centrifugal potential term for any arbitrary l-state. The approximate energy eigenvalues and unnormalized wave functions are obtained in closed forms using a simple shortcut of the NikiforovUvarov (NU) method. Further, we solve the KGYukawa problem for its exact numerical energy eigenvalues via the amplitude phase (AP) method to test the accuracy of the present solutions found by using the NU method. Our numerical tests using energy calculations demonstrate the existence of inter-dimensional degeneracy amongst the energy states of the KGYukawa problem. The dependence of the energy on the dimension D is numerically discussed for spatial dimensions D = 26.

Ikhdair, Sameer M; Hamzavi, Majid

doi: 10.1088/1674-1056/22/4/040302pmid: N/A

Approximate analytical bound-state solutions of the Dirac particle in the fields of attractive and repulsive RosenMorse (RM) potentials including the Coulomb-like tensor (CLT) potential are obtained for arbitrary spin-orbit quantum number . The Pekeris approximation is used to deal with the spin-orbit coupling terms (± 1)r2. In the presence of exact spin and pseudospin (p-spin) symmetries, the energy eigenvalues and the corresponding normalized two-component wave functions are found by using the parametric generalization of the NikiforovUvarov (NU) method. The numerical results show that the CLT interaction removes degeneracies between the spin and p-spin state doublets.

Jiang, Feng-Jian; Lü, Hai-Jiang; Yan, Xin-Hu; Shi, Ming-Jun

doi: 10.1088/1674-1056/22/4/040303pmid: N/A

A symmetric measure of quantum correlation based on the HilbertSchmidt distance is presented in this paper. For two-qubit states, we considerably simplify the optimization procedure so that numerical evaluation can be performed efficiently. Analytical expressions for the quantum correlation are attained for some special states. We further investigate the dynamics of quantum correlation of the system qubits in the presence of independent dissipative environments. Several nontrivial aspects are demonstrated. We find that the quantum correlation can increase even if the system state is suffering from dissipative noise. Sudden changes occur, even twice, in the time evolution of quantum correlation. There exists a certain correspondence between the evolution of quantum correlation in the systems and that in the environments, and the quantum correlation in the systems will be transferred into the environments completely and asymptotically.