Nonlinear Sigma Models in (1+2) Dimensions and an Infinite Number of Conserved Currents

In this Letter, we treat nonlinear sigma models such as the C P¹-model, Q P¹-model, etc. in 1+2 dimensions. For submodels of such models, we definitely construct an infinite number of nontrivial conserved currents. Our result is a generalization of Alvarez, Ferreira and Guillen.     

Design and optimal tuning of nonlinear PI compensators

In this paper, linear time-invariant single-input single-output (SISO) systems that are stabilizable by linear proportional and integral (PI) compensators are considered. For such systems, a five-parameter nonlinear PI compensator is proposed. The parameters of the proposed compensator are tuned by solving an optimization problem. The optimization problem always has a solution.Additionally, a general nonlinear PI compensator is proposed and is approximated by easy-to-compute compensators, for instance, a six-parameter nonlinear PI compensator. The parameters of the approximate compensators are tuned to satisfy an optimality condition. The superiority of the proposed nonlinear PI compensators over linear PI compensators is discussed and is demonstrated for two feedback systems.     

Half-line solutions of a nonlinear heat conduction problem

We solve a half-line problem for a nonlinear diffusion equation with a given time-dependent thermal conductivity at the origin. The problem reduces to a linear Volterra integral equation, which is solvable by Picard’s process of successive approximations. We analyze some explicit examples numerically. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 1, pp. 58–65, July, 2007.     

A New General Algebraic Method and Its Application to Shallow Long Wave Approximate Equations

A new general algebraic method is presented to uniformly construct a series of exact solutions for nonlinear evolution equations （NLEEs）. For illustration, we apply the new method to shallow long wave approximate equations and successfully obtain abundant new exact solutions, which include rational solitary wave solutions and rational triangular periodic wave solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.     

利用光折变晶体的电光、压电效应实现2×2光开关的原理

讨论了在光折变LiNbO3晶体中建立电场控制的 2× 2直通交换开关的原理设计方案。通过控制读出光栅时外加电场的大小使读出光满足或偏离布拉格条件 ,从而控制衍射效率为 1或 0 ,实现开关的交换和直通操作。全面考虑了电场作用下晶体的压电和电光效应 ,基于衍射效率公式和光栅的布拉格条件 ,给出了为获得最佳衍射效率比时外加电场及写入光束比与记录角度间的关系曲线     

Nonperturbative Operator Quantization of Strongly Nonlinear Fields

At present an algebra of strongly interacting fields is unknown. In this paper it is assumed that the operators of a strongly nonlinear field can form a non-associative algebra. It is shown that such an algebra can be described as an algebra of some pairs. The comparison of presented techniques with the Green's functions method in superconductivity theory is made. A possible application to the QCD and High-T _c superconductivity theory is discussed.     

双轴晶体主平面上倍频的相位匹配参量

根据折射率椭球方程及双光轴晶体中光波的传播与偏振特性，分析双轴晶体在主平面内激光倍频相位匹配的特性与方法，导出光波在主平面上传播时倍频的相位失配关系；给出双轴晶体中容许相位匹配倍频的相位匹配角及混频的有效非线性系数deff的表达式。利用可相位匹配的类型、相位匹配角公式和有效非线性系数deff表达式的表，容易对任意一具体晶体在一给定波长求出实际能实现相位匹配的类型或偏振组合，算出相位匹配角，比较不同的相位匹配类型或偏振组合的有效非线性系数，选择最佳的相位匹配类型与方向。从相位失配关系可以计算晶体主平面内倍频的接收角、接收光谱宽度等特性参量。     

OSCILLATORY AND ASYMPTOTIC BEHMIOUR OF A CLASS OF NONLINEAR DIFFERENTIALEQUATIONS OF THIRD ORDER

1IntroductionInthispaperwedealwithoscillatoryandnonoscillatorybehaviourofsolutionsofnonlinearthirdorderdifferentialequationsoftheformwherea,b,cEC([er,co),R),rrER,fEC(R,R)suchthatac2P>0fory/0and7>0isaquotientofoddintegers.From"Theoryofequations"tsee[1],itfollowsthattheequationwithconstantcoefficientsMoreover,allnonoscillatorysolutionsof(1.3)tendtozeroifandonlyifequatioll(l.3)hasanoscillatorysolution.Theseobservationsarefoundtobetruetoalargeextentformoregeneralequationsoftheformwherealb,cE…     

Crystal Growth and Nonlinear Optical Properties of 4－Br－4＇－Methoxychalcone（BMC）

Ｃｒｙｓｔａｌ Ｇｒｏｗｔｈ ａｎｄ Ｎｏｎｌｉｎｅａｒ Ｏｐｔｉｃａｌ Ｐｒｏｐｅｒｔｉｅｓ ｏｆ ４－Ｂｒ－４＇－Ｍｅｔｈｏｘｙｃｈａｌｃｏｎｅ（ＢＭＣ）￥ＣＡＯＹａｎｇ；ＺＨＵＺｈｉｄｏｎｇ；ＳＨＥＮＸｉａｏｐｉｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＣ...     

第Ⅱ类三态叠加多模叠加态光场等幂次2m+1次方Y压缩

构造了由多模虚相干态|{iZ_j}>_q、多模虚相干态的相反态|{-iZ_j}>_q和多模真空态|{O_j}>_q这三种不同的量子光场态的线性叠加所组成的第Ⅱ类三态叠加多模叠加态光场|ψ₂⁽³⁾>_q.利用多模压缩态理论,研究了态|ψ₂⁽³⁾>_q的广义非线性等幂次2m+1次方Y压缩特性.结果发现:在压缩次数N=2m+1(m=0,1,2,3,…,…)的条件下,只要各模的初始相位和态间的初始相位差分别满足一定的取值条件,态|ψ₂⁽³⁾>_q就可呈现出周期性变化的、任意奇数次的广义非线性等幂次N次方Y压缩效应.