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81.
82.
In this paper, new Jacobi elliptic function solutions of
multi-component mKdV equation are obtained directly in a unified
way. When the modulus m→1, those periodic solutions
degenerate as the corresponding hyperbolic function solutions.
Then, to the three-component mKdV equation, five types of
effective solution are presented in detail. 相似文献
83.
LI De-Sheng LUO Cheng-Xin 《理论物理通讯》2006,46(8)
In this paper, we improve the method for deriving Jacobi elliptic function solutions of nonlinear evolution equations given in Ref. [12] and apply it to the integrable higher-order Broer-Kaup system in (2 1)-dimensional spaces.Some new elliptic function solutions are obtained. 相似文献
84.
JI Li-Na QU Chang-Zheng 《理论物理通讯》2006,46(10)
The present paper discusses a class of nonlinear diffusion-convection equations with source. The method that we use is the conditional symmetry method. It is shown that the equation admits certain conditional symmetries for coefficient functions of the equations. As a consequence, solutions to the resulting equations are obtained. 相似文献
85.
86.
Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type for Lagrange systems
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Based on the invariance of differential equations under
infinitesimal transformations of group, Lie symmetries, exact
invariants, perturbation to the symmetries and adiabatic invariants
in form of non-Noether for a Lagrange system are presented. Firstly,
the exact invariants of generalized Hojman type led directly by Lie
symmetries for a Lagrange system without perturbations are given.
Then, on the basis of the concepts of Lie symmetries and higher
order adiabatic invariants of a mechanical system, the perturbation
of Lie symmetries for the system with the action of small
disturbance is investigated, the adiabatic invariants of generalized
Hojman type for the system are directly obtained, the conditions for
existence of the adiabatic invariants and their forms are proved.
Finally an example is presented to illustrate these results. 相似文献
87.
By using Lanczos exact diagonalization and quantum Monte Carlo combined with stochastic analytic continuation, we study the dynamical properties of the S = 1 antiferromagnetic Heisenberg chain with different strengths of bond disorder. In the weak disorder region, we find weakly coupled bonds which can induce additional low-energy excitation below the one-magnon mode. As the disorder increases, the average Haldane gap closes at δ∆ ~ 0.5 with more and more low-energy excitations coming out. After the critical disorder strength δc ~ 1, the system reaches a random-singlet phase with prominent sharp peak at ω = 0 and broad continuum at ω > 0 of the dynamic spin structure factor. In addition, we analyze the distribution of random spin domains and numerically find three kinds of domains hosting effective spin-1/2 quanta or spin-1 sites in between. These “spins” can form the weakly coupled longrange singlets due to quantum fluctuation which contribute to the sharp peak at ω = 0. 相似文献
88.
A unified approach to fuzzy modelling and robust synchronization of different hyperchaotic systems 总被引:2,自引:0,他引:2
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In this paper, a Takagi Sugeno (T-S) fuzzy model-based method is proposed to deal with the problem of synchronization of two identical or different hyperchaotic systems. The T S fuzzy models with a small number of fuzzy IF-THEN rules are employed to represent many typical hyperchaotic systems exactly. The benefit of employing the T-S fuzzy models lies in mathematical simplicity of analysis. Based on the T-S fuzzy hyperchaotic models, two fuzzy controllers arc designed via parallel distributed compensation (PDC) and exact linearization (EL) techniques to synchronize two identical hyperchaotic systems with uncertain parameters and two different hyperchaotic systems, respectively. The sufficient conditions for the robust synchronization of two identical hyperchaotic systems with uncertain parameters and the asymptotic synchronization of two different hyperchaotic systems are derived by applying the Lyapunov stability theory. This method is a universal one of synchronizing two identical or different hyperchaotic systems. Numerical examples are given to demonstrate the validity of the proposed fuzzy model and hyperchaotic synchronization scheme. 相似文献
89.
利用指数稳定半群生成元的谱理论,得到了判断指数稳定双系统在[0,∞)同时近似可观测的充分条件.{z1(t)=A1z1(t),z1(0)=x1,y1(t)=C1z1(t)2(t)=A2z2(t),z2(0)=x2,y2(t)=C2z2(t) 相似文献
90.
一阶微分方程M(x,y)dx+N(x,y)dy=0不是全微分方程时,寻找它的积分因子成为求解方程的关键,但又是比较棘手的问题。针对这一情况,本文通过对方程的积分因子存在的充要条件定理的证明,利用定理结论求解积分因子,进而求出其通解,是一种行之有效又直观方便的方法,从而达到化难为易的目的,而且定理结论具有一般性,可以进行推广,使求积分因子时不再盲目,变得有规可循。 相似文献