Nonlinear amphibious vehicle rolling under regular waves and wind load is analyzed by a single degree of freedom system.Considering nonlinear damping and restoring moments,a nonlinear rolling dynamical equation of amp...Nonlinear amphibious vehicle rolling under regular waves and wind load is analyzed by a single degree of freedom system.Considering nonlinear damping and restoring moments,a nonlinear rolling dynamical equation of amphibious vehicle is established.The Hamiltonian function of the nonlinear rolling dynamical equation of amphibious vehicle indicate when subjected to joint action of periodic wave excitation and crosswind,the nonlinear rolling system degenerates into being asymmetric.The threshold value of excited moment of wave and wind is analyzed by the Melnikov method.Finally,the nonlinear rolling motion response and phase portrait were simulated by four order Runge-Kutta method at different excited moment parameters.展开更多
The generalized one-dimensional Fokker-Planck equation is analyzed via potential symmetry method and the invariant solutions under potential symmetries are obtained. Among those solutions, some are new and first repor...The generalized one-dimensional Fokker-Planck equation is analyzed via potential symmetry method and the invariant solutions under potential symmetries are obtained. Among those solutions, some are new and first reported.展开更多
An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be f...An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be found by this new method, which include kink-shaped soliton solutions, bell-shaped soliton solutions and new solitary wave.The new method can be applied to other nonlinear equations in mathematical physics.展开更多
In this paper, we investigate the global behavior of the difference equation xn＋1=1-2n/A＋∑k i=1xn-iwith the A ∈ （-∞,-1） is a real number, k is a positive integer and the initial conditions x_k x0 ∈ （-∞, 0].
Recently, many important nonlinear partial differential equations arising in the applied physical and mathematical sciences have been tackled by a popular approach, the so-called Exp-function method. In this paper, we...Recently, many important nonlinear partial differential equations arising in the applied physical and mathematical sciences have been tackled by a popular approach, the so-called Exp-function method. In this paper, we present some shortcomings of this method by analyzing the results of recently published papers. We also discuss the possible improvement of the effectiveness of the method.展开更多
Suppression of spiral wave and turbulence in the complex Cinzburg-Landau equation （CCLE） plays a prominent role in nonlinear science and complex dynamical system. In this paper, the nonlinear behavior of the propose...Suppression of spiral wave and turbulence in the complex Cinzburg-Landau equation （CCLE） plays a prominent role in nonlinear science and complex dynamical system. In this paper, the nonlinear behavior of the proposed drive-response system, which consists of two coupled OGLEs, is investigated and controlled by a state error feedback controller with the lattice Boltzmann method. First, spiral wave appropriate parameters of the response system under the no-flux and turbulence are, respectively, generated by selecting boundary and perpendicular gradient initial conditions. Then, based on the random initial condition, the target wave yielded by introducing spatially localized inhomogeneity into the drive system is applied on the above response system. The numerical simulation results show that the spiral wave and turbulence existing in the response system could be successfully eliminated by the target wave in the drive system during a short evolution time. Furthermore, it turns out that the transient time for the drive course is related to the control intensity imposed on the whole media.展开更多
It is known that the one-dimensional nonlinear heat equation ut ： f（u）x1x1, f＇（u） 〉 0, u（±∞, t） ： u, u＋ ≠ u- has a unique self-similar solution u（x1/√1＋t）. In multi-dimensional space, （x1/√1＋t...It is known that the one-dimensional nonlinear heat equation ut ： f（u）x1x1, f＇（u） 〉 0, u（±∞, t） ： u, u＋ ≠ u- has a unique self-similar solution u（x1/√1＋t）. In multi-dimensional space, （x1/√1＋t） is called a planar diffusion wave. In the first part of the present paper, it is shown that under some smallness conditions, such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation： ut -△f（u） = 0, x ∈ R^n. The optimal time decay rate is obtained. In the second part of this paper, it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with damping： utt ＋ ut - △f（u） = 0, x ∈ R^n. The time decay rate is also obtained. The proofs are given by an elementary energy method.展开更多
基金The Pre-research Project of the General Armament DepartmentThe Science Fund of North University of China(No.20130105)
文摘Nonlinear amphibious vehicle rolling under regular waves and wind load is analyzed by a single degree of freedom system.Considering nonlinear damping and restoring moments,a nonlinear rolling dynamical equation of amphibious vehicle is established.The Hamiltonian function of the nonlinear rolling dynamical equation of amphibious vehicle indicate when subjected to joint action of periodic wave excitation and crosswind,the nonlinear rolling system degenerates into being asymmetric.The threshold value of excited moment of wave and wind is analyzed by the Melnikov method.Finally,the nonlinear rolling motion response and phase portrait were simulated by four order Runge-Kutta method at different excited moment parameters.
文摘The generalized one-dimensional Fokker-Planck equation is analyzed via potential symmetry method and the invariant solutions under potential symmetries are obtained. Among those solutions, some are new and first reported.
文摘An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be found by this new method, which include kink-shaped soliton solutions, bell-shaped soliton solutions and new solitary wave.The new method can be applied to other nonlinear equations in mathematical physics.
文摘In this paper, we investigate the global behavior of the difference equation xn＋1=1-2n/A＋∑k i=1xn-iwith the A ∈ （-∞,-1） is a real number, k is a positive integer and the initial conditions x_k x0 ∈ （-∞, 0].
文摘Recently, many important nonlinear partial differential equations arising in the applied physical and mathematical sciences have been tackled by a popular approach, the so-called Exp-function method. In this paper, we present some shortcomings of this method by analyzing the results of recently published papers. We also discuss the possible improvement of the effectiveness of the method.
基金Supported by the National Natural Science Foundations of China under Grant Nos.61202051,11272132the Special Fund for Basic Scientific Research of Central CollegesChina University of Geosciences Wuhan under Grant Nos.CUG110828 and CUG130416
文摘Suppression of spiral wave and turbulence in the complex Cinzburg-Landau equation （CCLE） plays a prominent role in nonlinear science and complex dynamical system. In this paper, the nonlinear behavior of the proposed drive-response system, which consists of two coupled OGLEs, is investigated and controlled by a state error feedback controller with the lattice Boltzmann method. First, spiral wave appropriate parameters of the response system under the no-flux and turbulence are, respectively, generated by selecting boundary and perpendicular gradient initial conditions. Then, based on the random initial condition, the target wave yielded by introducing spatially localized inhomogeneity into the drive system is applied on the above response system. The numerical simulation results show that the spiral wave and turbulence existing in the response system could be successfully eliminated by the target wave in the drive system during a short evolution time. Furthermore, it turns out that the transient time for the drive course is related to the control intensity imposed on the whole media.
基金Acknowledgements He＇s research is supported in part by National Basic Research Program of China （Grant No. 2006CB805902）. Huang＇ research is supported in part by National Natural Science Foundation of China for Distinguished Youth Scholar （Grant No. 10825102）, NSFC-NSAF （Grant No. 10676037） and National Basic Research Program of China （Grant No. 2006CB805902）.
文摘It is known that the one-dimensional nonlinear heat equation ut ： f（u）x1x1, f＇（u） 〉 0, u（±∞, t） ： u, u＋ ≠ u- has a unique self-similar solution u（x1/√1＋t）. In multi-dimensional space, （x1/√1＋t） is called a planar diffusion wave. In the first part of the present paper, it is shown that under some smallness conditions, such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation： ut -△f（u） = 0, x ∈ R^n. The optimal time decay rate is obtained. In the second part of this paper, it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with damping： utt ＋ ut - △f（u） = 0, x ∈ R^n. The time decay rate is also obtained. The proofs are given by an elementary energy method.
