相对转动非线性动力学方程的稳定性及在一类非线性弹性系数下的解

建立一类含非线性弹性力的二端面转轴相对转动非线性动力学方程.对相对转动非线性自治方程进行定性分析，研究方程的稳定性.用参数变换法求得相对转动非线性非自治方程在强迫激励下的高次近似解.     

相对转动非线性动力系统的稳定性与强迫激励下的近似解

研究相对转动非线性动力系统的运动稳定性.建立具有一般广义阻尼力和外扰激励的一类两质量相对转动非线性动力系统的动力学方程.研究相对转动非线性动力自治系统的稳定性，证明系统在一定条件下可发生闭轨分岔.应用多尺度法得到强迫激励下非自治系统的近似解. 关键词： 相对转动 非线性动力系统 运动稳定性 近似解     

耦合相对转动非线性动力系统的稳定性与近似解

研究了一类含三次非线性耦合项的相对转动非线性动力系统的动力学行为. 建立了具有非线性弹性力、广义摩阻力耦合项的系统动力学方程. 运用多尺度法求解谐波激励下耦合非自治系统的近似解,通过讨论系统的主共振和内共振特性,分析了耦合项对系统响应的影响. 应用奇异性理论研究了主振稳态响应分岔方程的稳定性,得到了系统的转迁集和分岔曲线的拓扑结构. 关键词： 相对转动 非线性耦合动力系统 奇异性理论 稳定性     

一类相对转动非线性动力学模型的近似解

研究了一类具有非线性阻尼力和强迫周期力项的相对转动非线性动力学模型. 首先构造一个同伦映射, 其次决定方程的初始近似, 最后通过同伦映射方法得到了对应模型的任意次近似解. 关键词： 相对转动 非线性动力系统 近似解     

一类非线性相对转动动力系统的平衡稳定性及组合谐波近似解

建立一类含广义非线性弹性力的两质量相对转动系统的非线性动力学方程. 应用变量梯度法构造李雅普诺夫函数,研究相对转动非线性自治系统的稳定性. 应用摄动法求得相对转动非线性非自治系统在两种不同频率谐波共同激励下的组合谐波响应的近似解. 关键词： 相对转动 非线性动力系统 稳定性 组合谐波响应     

一类谐波激励相对转动非线性动力系统的稳定性与近似解

建立具有一般非线性弹性力、广义摩阻力和谐波激励的一类相对转动非线性动力系统的动力学方程. 对相对转动非线性自治系统进行定性分析,通过构造Lyapunov函数研究自治系统奇点的稳定性. 运用多尺度法求解谐波激励下非自治系统在几种不同共振响应下的近似解,同时分析了主振系统稳态运动的稳定性. 关键词： 相对转动 非线性动力系统 Lyapunov函数 稳定性     

Lam函数和非线性演化方程的扰动方法

利用小扰动方法对非线性演化方程作展开得到原始方程的各级近似方程.应用Jacobi椭圆函 数展开法求得了零级近似方程的准确解，并由此得到一级近似方程和二级近似方程分别满足 齐次Lam方程和非齐次Lam方程，应用Lam函数和Jacobi椭圆函数展开法可以分别求得一级近似方程和二级近似方程的准确解.这样，就求得了非线性演化方程的多级准确解. 关键词： Jacobi椭圆函数 Lam函数 多级准确解 非线性演化方程 扰动方法     

Lam函数和非线性演化方程的扰动方法

利用小扰动方法对非线性演化方程作展开得到原始方程的各级近似方程 .应用Jacobi椭圆函数展开法求得了零级近似方程的准确解 ,并由此得到一级近似方程和二级近似方程分别满足齐次Lam 方程和非齐次Lam 方程 ,应用Lam 函数和Jacobi椭圆函数展开法可以分别求得一级近似方程和二级近似方程的准确解 .这样 ,就求得了非线性演化方程的多级准确解 .     

Lamé函数和非线性演化方程的扰动方法

利用小扰动方法对非线性演化方程作展开得到原始方程的各级近似方程.应用Jacobi椭圆函数展开法求得了零级近似方程的准确解,并由此得到一级近似方程和二级近似方程分别满足齐次Lamé方程和非齐次Lamé方程,应用Lamé函数和Jacobi椭圆函数展开法可以分别求得一级近似方程和二级近似方程的准确解.这样,就求得了非线性演化方程的多级准确解.     

微扰的耦合非线性薛定谔方程的近似求解

将直接微扰方法应用于可积的含修正项的非线性薛定谔方程，通过近似解与精确解的比较确定了直接微扰方法的可靠性.继而，将该方法应用于微扰的耦合非线性薛定谔方程，并获得了该微扰方程的可靠的近似解. 关键词： 直接微扰方法 微扰 耦合非线性薛定谔方程 近似解     

含时旋转磁场中的两耦合粒子的纠缠演化(英文)

我们研究了含时旋转磁场中海森堡XXX模型下的双量子比特的动力学演化情况.基于此非自治系统的代数结构,我们用代数动力学方法求得了系统的精确解析解.在此基础上,进一步研究了在不同初态下系统的纠缠测度随时间的演化,发现纠缠测度由系统的初态的系数和耦合强度决定.     

Entanglement Evolution of Two-Coupled Spins in a Time-Dependent Rotating Magnetic Field

We study the dynamics evolution of a two-qubit Heisenberg XXX spin chain under a time-dependent rotating magnetic field. Based on the algebraic structure of the non-autonomous system, the exact solution of the Schrödinger equation is obtained by using the method of algebraic dynamics. Based on the time-dependent analytical solution, we further study the entanglement evolution between the two coupled spins for different initial states, and find that the entanglement is determined by the coefficients of the initial state and the coupling constant $J$ of the system.     

Entanglement dynamics in atom-field interaction in the presence of noise: a special application of the Burshtein equation

The entanglement dynamics in a system of the interaction of an atom with a single-mode thermal field in the presence of noise is studied by the Jaynes-Cummings model. Two-state random phase telegraph noise is considered as the noise in the interaction and an exact solution to the model under this noise is obtained by the Burshtein equation. Although the Burshtein equation is applicable for laser-atom interactions, it is shown that it can be applied to atom-thermal field system as a special case. The solution is used to investigate the entanglement dynamics of the atom-field interaction by calculating a lower bound on concurrence. It is found that the entanglement is a non monotonic function of the intensity of the noise. The degree of the entanglement decreases to a minimum value for an optimal intensity of the noise and then increases for a sufficiently large intensity. Moreover, intense noise may generate stronger entanglement compared with the absence of noise.     

Modulated Wave Packets in DNA and Impact of Viscosity

We study the nonlinear dynamics of a DNA molecular system at physiological temperature in a viscous media by using the Peyrard-Bishop model. The nonlinear dynamics of the above system is shown to be governed by the discrete complex Cinzburg-Landau equation. In the non-viscous limit, the equation reduces to the nonlinear Schroedinger equation. Modulational instability criteria are derived for both the cases. On the basis of these criteria, numerical simulations are made, which confirm the analytical predictions. The planar wave solution used as the initial condition makes localized oscillations of base pairs and causes energy localization. The results also show that the viscosity of the solvent in the surrounding damps out the amplitude of wave patterns.     

Bunching of particles with nonzero longitudinal emittance

The dynamics of the bunching of particles with nonzero longitudinal emittance is studied in plane geometry. A self-consistent solution to the model time-dependent kinetic equation is obtained for a collisionless system of particles. The solution is shown to be nonunique. Two acceleration modes resulting in the creation of a virtual cathode and, therefore, in the bunching of particles are basically possible.     

Adiabatic Elimination in Quantum Stochastic Models

We consider a physical system with a coupling to bosonic reservoirs via a quantum stochastic differential equation. We study the limit of this model as the coupling strength tends to infinity. We show that in this limit the solution to the quantum stochastic differential equation converges strongly to the solution of a limit quantum stochastic differential equation. In the limiting dynamics the excited states are removed and the ground states couple directly to the reservoirs.     

On the exact solutions of nonlinear Schrödinger equation with spin current

An integrable nonlinear Schrödinger (NLS) equation driven by spin polarized current governing the magnetization dynamics of a ferromagnetic nanowire is considered. The exact soliton solution of the NLS equation propagating along the direction of wire axis which is also the current direction along which nonuniform magnetization occurs is obtained through the application of exponential function method. The solution of the system admits a class of solitons such as kink and periodic solitons in the nanowire along the direction of the electric current.     

An integrable 3D model for Heisenberg ferromagnetic spin system with biquadratic interactions

We formulate a model Hamiltonian to a 3D Ferromagnetic spin system incorporating biquadratic interactions. The dynamics is represented by a higher order (3+1) dimensional integrable nonlinear Schrödinger equation. We construct the Lax pair associate with the system and find multisoliton solutions using Darboux transformation(DT). We bilinearize the equation using Hirota’s bilinearization procedure and find one soliton solution.     

受简谐激励载流导线的三次超谐共振

研究受简谐激励的二长直电流间载流导线的三次超谐共振问题,应用动力学方法建立载流导线受外部激励和安培力的Duffing方程.根据非线性振动的多尺度解法,得到系统满足三次超谐共振情况的一次近似解以及对应的定常解,并对其进行数值计算.分析直流、交流、调谐值、张力、激励等对系统的影响.