非线性基底势对离散非线性晶格孤波动力学性质的影响

使用一种简化的准离散多重尺度法,研究了具有非线性基底势的一维离散非线性晶格的孤波解, 表明孤波能够在这种一维非线性晶格链中存在,而且非线性基底势对孤波的载波频率、群速度、振幅等动力学性质都将产生影响。 另一方面,我们还对非线性动力学方程进行了数值求解, 发现用简化的准离散多重尺度法得到的近似解与精确的计算机数值计算结果符合得较好。     

阻尼作用下一维非线性单原子链中的孤子

利用多重尺度法,研究了弱阻尼作用下一维非线性单原子链中的波动行为,发现在O(ε)级阻尼作用下其格波幅度减小,群速变慢.在晶格动力学中导出了参数耗散型非线性Schrdinger方程,对方程进行解析求解.结果表明在O(ε)级阻尼作用下一维非线性单原子链中的格孤波为传播的包络孤子;在O(ε2)级阻尼作用下,格孤波为钟状或扭结的孤子.     

阻尼作用下一维非线性单原子链中的孤子

利用多重尺度法,研究了弱阻尼作用下一维非线性单原子链中的波动行为,发现在O(ε)级阻尼作用下其格波幅度减小,群速变慢.在晶格动力学中导出了参数耗散型非线性Schr?dinger方程,对方程进行解析求解.结果表明:在O(ε)级阻尼作用下一维非线性单原子链中的格孤波为传播的包络孤子;在O(ε²)级阻尼作用下,格孤波为钟状或扭结的孤子.     

一维金刚石结构晶格的非线性局域模

用多重尺度法研究了质量均匀相互作用力交替变化的原子链形成的非线性局域振动模式,这 种原子链模拟了金刚石结构晶格沿〈111〉晶向或一维分子链的振动,通过多重尺度展开分 析得出,原子位移分布服从微扰的非线性Schrdinger方程,求得了相应的定态解和传播解 ,其结果与相互作用力相同质量交替分布的另一种形式的一维双原子晶格的结果有所不同, 其原因是金刚石结构晶格的对称性相对差些. 关键词： 金刚石结构 非线性局域模 多重尺度法     

Kerr类非线性介质周期结构中的慢Bragg孤子

在耦合模理论的基础上,给出了一维无限大Kerr类非线性介质周期结构中的孤波解,并且指出,孤波的振幅依赖于入射频率以及脉宽两个参量.同时也证明,在布拉格共振极限条件下,孤波解可以简化成所谓的“隙孤子”解或是“慢布拉格孤子”解 关键词： 孤波 慢布拉格孤子 隙孤子 耦合模理论     

求解非线性差分方程孤立波解的直接代数法

推广了求解非线性差分方程孤立波解的直接代数法.用此方法研究了Hybrid晶格方程，借助于符号计算Maple,得到它的新孤波解.这种方法也可用于求解其他的差分方程. 关键词： 微分-差分方程 Hybrid晶格方程 行波解 孤     

一维铁磁链中量子孤波的能级和磁矩

使用Hartree近似和一种简化的准离散多标度方法,研究了具有交换作用和经典磁矩相互作用的一维铁磁链中的量子孤波解. 这种一维铁磁链中不仅存在着运动的量子孤波,也存在着静态的量子孤波(即量子内禀局域模).利用所获得的量子孤波解,进一步研究了量子孤波的能级和由量子孤波所携带的磁矩. 研究表明,量子孤波的能量和磁矩都是量子化的,这些结果为正确理解磁性材料中像磁滞回线的量子台阶等宏观量子特性提供了一条可能的途径.     

大尺度浅水波方程中相互调制的非线性波

基于一般的浅水波方程, 根据大尺度正压大气的特点, 得到无量纲的控制大尺度大气的动力学非线性方程组. 利用多尺度法, 由无量纲的动力学方程组导出了扰动位势的非线性控制方程. 采用椭圆方程构造该扰动位势控制方程的解, 获得了扰动位势和速度的多周期波与冲击波(爆炸波) 并存的解析解. 扰动位势的解表明经向和纬向具有不同周期和波长的周期波, 且都受纬向孤波的调制; 速度的解表明大尺度大气流动存在气旋和反气旋周期性分布的现象. 关键词： 浅水波方程 大尺度正压大气 解析解 非线性波     

计及次近邻作用时一维格子的非线性元激发

同时考虑次近邻谐振相互作用和三次方、四次方非谐相互作用,利用多重尺度结合准离散近似方法去计算晶格振动行为,发现一维非线性点阵中存在包络孤子及正扭结型包络孤子、反扭结型包络孤子,解释了自局域结构的幅度只取决于点阵中的固有参数的实验现象 关键词： 非线性点阵 非谐相互作用 扭结型包络孤子     

非线性长波方程组和Benjamin方程的新精确孤波解

在齐次平衡法、双曲正切函数法和辅助方程法的基础上引入一个新的辅助方程,并借助符号计算系统Mathematica来构造了非线性长波方程组和Benjamin方程的新精确孤波解, 这种方法也可用于寻找其他非线性发展方程的新的孤波解. 关键词： 新的辅助方程 非线性长波方程组 Benjamin方程 孤波解     

The nonlinear group representation method in the nonlinear spinor theory

Nonlinear spinor equations are derived in the paper by the nonlinear symmetry-group representation method. The basic field transforms according to the linear spinor representation of the orthochronous Lorentz group Lt. The internal symmetry group G^r is realized as a group of nonlinear transformations of the field . The invariant nonlinear spinor equations constituting the group G^r are found in terms of the covariant derivative. The group SU(2) is considered as an example.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 49–55, December, 1972.The author thanks D. D. Ivanenko and D. F. Kurdgelaidze for stimulating discussions and support.     

Estimating the nonlinear resonant frequency of a single pile in nonlinear soil

Analytical expressions are determined for the nonlinear resonant frequency (or natural frequency) of the fundamental lateral mode of a pile. A pile with a floating toe, with and without pile cap is considered in this paper. The influence of a nonlinear soil spring model that varies with depth and a nonlinear damping model that is strain amplitude dependent is considered. A non-dimensional equation of motion for the system dynamics is derived from an energy based formulation. This equation is a Duffing's type nonlinear differential system that has nonlinear damping. Harmonic balance with numerical continuation is employed to determine the nonlinear resonance curves of the system. Comparison with some experimental results is made.     

Absolute determination of the nonlinear susceptibilityχ3 via two-beam nonlinear interferometry

A two-beam nonlinear interferometric technique is described whereby the amplitude and sign of both the real and imaginary parts of the nonlinear susceptibility _χ3 may be determined. Moreover, this technique permits an extremely precise determination of the electronic and molecular contributions to _χ3. Hence, we ascertain the electronic fraction of the Kerr constants of CS₂ and C₆H₆ to be 12.7 ± 1.1% and 19.8 ± 0.8%, respectively. These results provide a basis for the comparison of nonlinear refractivity and frequency-mixing measurements in these materials and an accurate means for the absolute calibration of a variety of measurements of _χ3.     

Polarization nonlinear optics of quadratically nonlinear azopolymers

The polarization properties of second harmonic and sum-frequency signals generated by femtosecond laser pulses in films of polymers containing covalent groups of an azobenzothiazole chromophore polarized by an external electric field are investigated. It is shown that the methods of polarization nonlinear optics make it possible to determine the structure of oriented molecular dipoles and reveal important properties of the motion of collectivized π electrons in organic molecules with strong optical nonlinearities. The polarization measurements show that the tensor of quadratic nonlinear optical susceptibility of chromophore fragments oriented by an external field in macromolecules of the noted azopolymers has a degenerate form. This is indicative of a predominantly one-dimensional character of motion of collectivized π electrons along an extended group of atoms in such molecules.     

Integrability of linear and nonlinear evolution equations and the associated nonlinear fourier transforms

The inverse spectral method is a nonlinear Fourier transform method for solving certain equations. Here, we emphasize that such transforms should be considered in their own right. We also elucidate further the connection between the Fourier transform and inverse spectral methods by establishing that linear equations can also be solved through the inverse spectral method.     

Analysis on the effect of nonlinear polarization evolution in nonlinear amplifying loop mirror

By considering the cross phase modulation (XPM) between the two orthogonal poparization components,the nonlinear birefringence and nonlinear polarization evolution (NPE) in highly-nonlinear fiber (HNLF),as well as the unequal evolutions of the state of polarization (SOP) between the clockwise (CW) and counter-clockwise (CCW) waves in a nonlinear amplifying loop mirror (NALM) are analyzed. It is pointed out that the traditional cosine expression is no longer valid for the power transmission of NALM due to uncompleted interference under the high power condition. The analytical expression considering NPE effect is derived, and the experimental result is presented.     

On the investigation of nonlinear waves of the Hirota and the Maxwell–Bloch equation in nonlinear optics

In this paper, considering the Hirota and Maxwell-Bloch (H-MB) equations which is governed by femtosecond pulse propagation through two-level doped fibre system, we construct the Darboux transformation of this system through linear eigenvalue problem. Using this Daurboux transformation, we generate multi-soliton, positon, and breather solutions (both bright and dark breathers) of the H-MB equations. Finally, we also construct the rogue wave solutions of the above system.     

Engineering the nonlinear phase shift

We treat the nonlinear phase shift response in the weak perturbation limit as a linear digital filter that can be synthesized into the values of its poles and zeros and mapped onto an optical architecture. This procedure results in a significant enhancement in the nonlinear sensitivity with a response that is robust to frequency changes within the filter passband. A precompensation technique can be used to reduce distortions under strongly driven nonlinear operation to achieve a larger phase shift. We also show that nonlinear sensitivity improves with increasing filter group delay and can be increased within constant linear bandwidth by use of higher-order filters.     

Propagation of nonlinear waves in bi-inductance nonlinear transmission lines

We consider a one-dimensional modified complex Ginzburg-Landau equation, which governsthe dynamics of matter waves propagating in a discrete bi-inductance nonlineartransmission line containing a finite number of cells. Employing an extended Jacobielliptic functions expansion method, we present new exact analytical solutions whichdescribe the propagation of periodic and solitary waves in the considered network.