Chinese Physics B

Xiao-Jing, Li

doi: 10.1088/1674-1056/19/3/030201pmid: N/A

A class of oscillator of the El Niño-Southern oscillation model is considered. Using Mawhin's continuation theorem, a result on the existence of periodic solutions for ENSO model is obtained.

Jia-Qi, Mo; Yi-Hua, Lin; Wan-Tao, Lin

doi: 10.1088/1674-1056/19/3/030202pmid: N/A

A reduces equation of the Kelvin wave is considered. By using the homotopic mapping solving method, the approximate solution is obtained. The homptopic mapping method is an analytic method, the obtained solution can analyse operations sequentially.

Wei-Zhen, Pan; Xiang-Jiong, Song; Jun, Yu

doi: 10.1088/1674-1056/19/3/030203pmid: N/A

The dynamical behaviour of the generalized Korteweg-de Vries (KdV) equation under a periodic perturbation is investigated numerically. The bifurcation and chaos in the system are observed by applying bifurcation diagrams, phase portraits and Poincaré maps. To characterise the chaotic behaviour of this system, the spectra of the Lyapunov exponent and Lyapunov dimension of the attractor are also employed.

Chun-Yu, Zhao; Yi-Min, Zhang; Bang-Chun, Wen

doi: 10.1088/1674-1056/19/3/030301pmid: N/A

We derive the non-dimensional coupling equation of two exciters, including inertia coupling, stiffness coupling and load coupling. The concept of general dynamic symmetry is proposed to physically explain the synchronisation of the two exciters, which stems from the load coupling that produces the torque of general dynamic symmetry to force the phase difference between the two exciters close to the angle of general dynamic symmetry. The condition of implementing synchronisation is that the torque of general dynamic symmetry is greater than the asymmetric torque of the two motors. A general Lyapunov function is constructed to derive the stability condition of synchronisation that the non-dimensional inertia coupling matrix is positive definite and all its elements are positive. Numeric results show that the structure of the vibrating system can guarantee the stability of synchronisation of the two exciters, and that the greater the distances between the installation positions of the two exciters and the mass centre of the vibrating system are, the stronger the ability of general dynamic symmetry is.

Chang, Liu; Peng, Chang; Shi-Xing, Liu; Yong-Xin, Guo

doi: 10.1088/1674-1056/19/3/030302pmid: N/A

This paper constructs an almost-Poisson structure for the non-self-adjoint dynamical systems, which can be decomposed into a sum of a Poisson bracket and the other almost-Poisson bracket. The necessary and sufficient condition for the decomposition of the almost-Poisson bracket to be two Poisson ones is obtained. As an application, the almost-Poisson structure for generalised Chaplygin's systems is discussed in the framework of the decomposition theory. It proves that the almost-Poisson bracket for the systems can be decomposed into the sum of a canonical Poisson bracket and another two noncanonical Poisson brackets in some special cases, which is useful for integrating the equations of motion.

Hui-Bin, Wu; Feng-Xiang, Mei

doi: 10.1088/1674-1056/19/3/030303pmid: N/A

This paper studies the symmetry of Lagrangians of nonholonomic systems of non-Chetaev's type. First, the definition and the criterion of the symmetry of the system are given. Secondly, it obtains the condition under which there exists a conserved quantity and the form of the conserved quantity. Finally, an example is shown to illustrate the application of the result.

Jin-Chao, Cui; Yao-Yu, Zhang; Xin-Fang, Yang; Li-Qun, Jia

doi: 10.1088/1674-1056/19/3/030304pmid: N/A

Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system are investigated. Appell equations and differential equations of motion for a variable mass holonomic system are established. A new expression of the total first derivative of the function with respect of time t along the systematic motional track curve, and the definition and the criterion of Mei symmetry for Appell equations under the infinitesimal transformations of groups are given. The expressions of the structural equation and Mei conserved quantity for Mei symmetry in Appell are obtained. An example is given to illustrate the application of the results.

Xin-Fang, Yang; Li-Qun, Jia; Jin-Chao, Cui; Shao-Kai, Luo

doi: 10.1088/1674-1056/19/3/030305pmid: N/A

Mei symmetry and Mei conserved quantity of Nielsen equations for a non-holonomic, non-conservative system of Chetaev's type with variable mass are studied. The differential equations of motion of the Nielsen equation for the system, the definition and criterion of Mei symmetry, and the condition and the form of Mei conserved quantity deduced directly by Mei symmetry for the system are obtained. An example is given to illustrate the application of the results.

Yin-Long, Zhao; Yin-Ping, Liu; Zhi-Bin, Li

doi: 10.1088/1674-1056/19/3/030306pmid: N/A

Recently the (G/G)-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the (G/G)-expansion method is a special form of the truncated Painlevé expansion method by introducing an intermediate expansion method. Then the generalized (G/G)(G/G) expansion method is naturally derived from the standpoint of the nonstandard truncated Painlevé expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the (G/G)-expansion method.

Wei, Li; Shi-Bing, Liu; Wei, Yang

doi: 10.1088/1674-1056/19/3/030307pmid: N/A

A new approach is developed to solve the Green's function that satisfies the Hehmholtz equation with complex refractive index. Especially, the Green's function for the Helmholtz equation can be expressed in terms of a one-dimensional integral, which can convert a Helmholtz equation into a Schrödinger equation with complex potential. And the Schrödinger equation can be solved by Feynman path integral. The result is in excellent agreement with the previous work.