(2+1)维Korteweg-de Vries方程的传播孤子及混沌行为

利用一个投射方程和变量分离法,得到了(2+1)维Korteweg-de Vries(KdV)方程的新显式精确解.根据得到的孤立波解,构造出KdV方程的传播孤子结构.利用一个新的混沌系统研究了孤子的混沌行为。     

含外力项的广义KdV方程的类孤子解

本文利用广义KP方程的B?cklund变换,获得了含外力项的广义KdV方程u_t+6uu_x+u_xxx+6f(t)u=g(t)+x(f′+12f²) (1)的类孤子解。 关键词：     

(2+1)维色散长波方程的新精确解及其复合波激发

利用Riccati方程展开法和变量分离法,得到了(2+1)维色散长波方程的变量分离解.根据得到的孤波解,构造出该方程新颖的复合波局域结构,研究了复合波随时间的演化.     

推广的KdV方程的孤波解

本文研究了推广的KdV方程 u_t+2μuu_x+v_3x+δu_5x=0(μvδ≠0) (1)的精确孤子解,得到了(1)式的一些新的孤波解,对文献[10]的若干结论作了补充与修正。 关键词：     

(2+1)维非线性KdV方程的新孤子结构

通过选取另一类种子解，给出了(2+1)维非线性KdV方程的一类变量分离新解.适当地选择变量分离新解中的任意函数和条件函数，揭示了一类新型孤子结构，如周期性孤波结构、环状孤子结构、曲线型孤子结构等.可以发现(2+1)维非线性KdV方程存在的这类新型孤子结构，是无法通过以往文献中给出的通用变量分离表达式得到的，而且这类新型孤子结构对于实际自然现象的解释有积极的意义. 关键词： 变量分离法 (2+1)维非线性KdV方程 新孤子结构     

在Jacobi正弦周期波背景下的dromion孤立波及其演化

利用改进的Riccati方程映射法、Bcklund变换法和变量分离法，得到了(2+1)维广义Breor-Kaup(GBK)方程的新显式精确解.根据得到的解，找到了GBK方程的复合波，并进一步研究了在Jacobi正弦周期波背景下dromion孤立波的演化. 关键词： 改进的映射法 广义Breor-Kaup方程 复合波 Jacobi正弦周期波     

浅水体系中的多孤立波

形式分离变量法被推广应用于寻求不可积模型的多孤立波解.特别地,应用形式分离变量法于三个描述浅水体系的非线性方程:推广WhithamBroerKaup(WBK)方程、2+1维耦合KortewegdeVries(KdV)方程和1+1维耦合KdV方程,给出了这些体系的明显的解析的多孤立波解 关键词： 浅水体系 多孤立波 形式分离变量法 不可积模型     

变系数广义KdV方程新的类孤波解和精确解

用普通KdV方程作变换，构造变系数广义KdV方程的解，获得了变系数广义KdV方程新的Jacobi椭圆函数精确解、类孤波解、三角函数解和Weierstrass椭圆函数解. 关键词： KdV方程 变系数广义KdV方程 类孤波解 精确解     

(3+1)维非线性Burgers系统的新的分离变量解及其局域激发结构与分形结构

将扩展的Riccati方程映射法推广到了(3+1)维非线性Burgers系统，得到了系统的分离变量解；由于在解中含有一个关于自变量(x,y,z,t)的任意函数，通过对这个任意函数的适当选取，并借助于数学软件Mathematica进行数值模拟，得到了系统的新而丰富的局域激发结构和分形结构.结果表明，扩展的Riccati方程映射法在求解高维非线性系统时，仍然是一种行之有效的方法，并且可以得到比(2+1)维非线性系统更为丰富的局域激发结构. 关键词： 扩展的Riccati方程映射法 (3+1)维非线性Burgers方程 局域激发结构 分形结构     

耦合KdV方程的双峰孤立子及其稳定性

利用扩展双曲函数法求解了耦合KdV方程,得到了6类精确解,其中一类为具有双峰状结构的单孤子解.在不同的极限情况下,该解分别退化为耦合KdV方程的扭结状或钟状孤波解.文中对双峰孤立波的稳定性进行了数值研究,结果表明:耦合KdV方程的双峰孤立波在长波小振幅扰动和小振幅钟型孤立波扰动下,均稳定. 关键词： 耦合KdV方程 双峰孤立子 稳定性     

Influence of magnetization on lattice constants of 3d transition metal alloys

A simple relation is found in 3d transitional metal alloys between the lattice constant and the magnetization, which can be described with an equation: a(x) = a₀^A· (1 − x) + a₀^B. x + C μ(x). It is proposed that studies of lattice constants at high temperatures may serve as an experimental method to detect the existence of localized moments above T_c. The anomalous thermal expansion of the Invar alloy is explained as a result of the collapse of localized moments above T_c.     

非自治物质畸形波的传播操控

研究了(1+1)维的变系数Gross-Pitaevskii方程, 获得了该方程的精确畸形波解. 基于该精确畸形波解, 深入研究了非自治物质畸形波在随时间指数变化的相互作用下的传播动力学行为, 发现非自治畸形波除具有“来无影、去无踪”的不可预测特性外, 也可实现完全激发、抑制激发以及维持激发等操控. 研究表明, 畸形波操控的关键是对累积时间的最大值T_max 与峰值位置T₀ (或T_I,T_II)值大小关系的调节. 当T_max > T₀ (或T_I,T_II)时畸形波被快速地完全激发, 热原子团中的原子增加到凝聚体中. 当T_max = T₀ (或T_I,T_II) 时畸形波激发到最大振幅, 可以维持相当长的时间而不消失, 热原子团中的原子增加到凝聚体中. 当T_max < T₀ (或T_I,T_II)时畸形波没有充足的时间来激发而被抑制甚至消失, 凝聚体中的原子减少. 这些结果在理论和实际应用上具有启迪意义.     

高次柱面反射型太阳能聚光镜的光学设计

提出了一种新型高效太阳能聚光镜, 这种聚光镜用一组特定系数, a₂, a₄, a₆, a₈, a₁₀, a₁₂, a₁₄, a₁₆ 与 C的高次柱面内壁的一部分作为反射镜. 利用高次柱面方程和光反射定律, 推导出了在高次柱面内壁上太阳反射光束的方向矢量与高次柱面系数C, a₂,a₄, a₆, a₈, a₁₀, a₁₂, a₁₄, a₁₆的关系, 通过优化设计这些系数, 可以使入射到高次柱面内壁上的太阳光束反射后全部聚焦在一条与柱面母线平行的宽度很窄的线段上, 形成线聚光. 这组特定系数用粒子群优化算法求得, 并经计算机模拟证明其聚焦效果. 用这组特定系数的高次柱面作为聚光镜, 其对光的压缩比可达148倍, 其线性光斑可作为一种强光源或高温光源. 高次柱面反射镜可由金属或玻璃直接磨制而成, 也可由高次柱面骨架和铺设在骨架上的镀铝聚酯薄膜构成. 关键词： 太阳能聚光镜 高次柱面 多项式系数优化 线性聚焦     

Synthesis and characterization of HgBa2Can−1CunO2n+2+δ (n = 1, 2, and 3)

We have successfully prepared the first three members of the mercury-based superconducting compounds Hg--- Ba₂Ca_n−1Cu_nO_2n+2+δ, namely Hg---1201, Hg---1212 and Hg---1223 with high purity and very good quality. T he influence of the synthesis parameters is studied in detail. Using the sealed quartz tube method, very simple procedures are found to ensure a 100% reproducibility of nearly 100% pure Hg---1201 and 85–90% Hg---1212 and Hg---1223. Oxygen annealing of the sample Hg---1201 at 300°C for 18 h results in an enhancement of its critical temperature up to 97 K. The symmetry of the first and second members is tetragonal with lattice parameters a = 3.8831 (1) Å, C = 9.5357 (2) Å, and A = 3.8624 (1) Å, C = 12.7045 (2) Å, respectively. X-ray diffraction lines of Hg---1223 can be indexed in a tetragonal cell with a = 3.8564 (1) Å and C = 15.8564 (9) Å as well as in an orthorhombic cell with lattice parameters a = 5.4537 (1) Å, B = 5.4247 (1) Å, and C = 15.8505 (7) Å.     

Monte Carlo optimisation of correlated wave functions for normal two-electron systems

A simple, new type of correlated wave function is proposed for the studies of normal two-electron atomic systems: ψ(r₁, r₂) = Σc_mΦ_m(r₁, r₂) with Φ_m(r₁, r₂) = exp[−(r₁ + r₂)]/(br₁₂ + a)^m, where , a, b are non-linear variational parameters. A notable feature of this basis function is that only three terms are required within the framework of the Raleigh-Ritz variational principle to obtain fairly accurate energy eigenvalues and satisfactory cusp conditions. The non-linear variational parameters are optimised by using the Monte Carlo technique.     

Localized Excitations of (2+1)-Dimensional Korteweg-de Vries System Derived from a Periodic Wave Solution

With the aid of an improved projective approach and a linear variable separation method,new types of variable separation solutions (including solitary wave solutions,periodic wave solutions,and rational function solutions)with arbitrary functions for (2 1)-dimensional Korteweg-de Vries system are derived.Usually,in terms of solitary wave solutions and rational function solutions,one can find some important localized excitations.However,based on the derived periodic wave solution in this paper,we find that some novel and significant localized coherent excitations such as dromions,peakons,stochastic fractal patterns,regular fractal patterns,chaotic line soliton patterns as well as chaotic patterns exist in the KdV system as considering appropriate boundary conditions and/or initial qualifications.     

A new measurement of the weak magnetism term in the betaspectra of B and N

The betaspectra of ¹²B and ¹²N have been measured with a NaI crystal as spectrometer. Assuming a shape correction factor 1 + aW + bW² and b₋ = 1.106 × 10⁻⁴ MeV⁻², b₊ = −1.397 × 10⁻⁴ MeV⁻², the spectra yield a₋ = (+0.91 ± 0.11) × 10⁻² MeV⁻¹ and a₊ = (−0.07 ± 0.09) × 10⁻² MeV⁻. the a₋ − a₊ = (+0.98 ± 0.09) × 10⁻² MeV⁻¹ is in agreement with the weak magnetism prediction.     

Entropy of planar random surfaces on the lattice

We study planar random surfaces on a hypercubic lattice in two and three dimensions by Monte Carlo techniques. Our data are consistent with the formula n₀(A;C) A^b₀A, where n₀(A;C) is the number of planar random surfaces with area A and boundary C. We find b₀ = −1.4 ± 0.2, = 5.31 ± 0.03 (for d = 2) and b₀ = −1.5 ± 0.2, = 7.13 ± 0.05 (for d = 3). The values of b₀ disagree with those obtained from the Polyakov string model.     

Symbolic Computation and Construction of Soliton－Like Solutions to the（2＋l）－Dimensional Breaking Soliton Equation

Based on the computerized symbolic system Mapte, a new generalized expansion method of Riccati equation for constructing non-travelling wave and coefficient functions‘ soliton-like solutions is presented by a new general ansatz. Making use of the method, we consider the (2 1)-dimensional breaking soliton equation, ut buxxy 4buvx 4buxv = O,uv=vx, and obtain rich new families of the exact solutions of the breaking sofiton equation, including then on-traveilin~ wave and constant function sofiton-like solutions, singular soliton-like solutions, and triangular function solutions.