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When SiO〓-NH〓-Rh-Co complex was used to catalyze the hydroformylation of methyl methacrylate, an optimal conversion of 93.4% and optimal selectivity of 84.4% for the normal aldehyde were both obtained at Rh/Co ratio of 2/1, which were both higher than that catalyzed by SiO〓-SiNH〓-Rh and SiO〓-Si-NH〓-Co momometallic catalysts. Clearly a synergistic action between Rh and Co atoms presented in the complex.

我们以SiO〓-Si-NH〓-Rh-Co催化甲基丙烯酸甲酯的醛化反应,当催化剂中Rh/Co比为2/1时,催化活性最高,可达93.4%,对正构产物β-甲酰异丁酸酯的选择性达到84.4%,都高于单金属催化剂,表明了金属间存在相互作用。

Several important nonlinear equations of mathematical physics such as φ4 equation, Klein-Gordon equation, the approximate equations of sine-Gordon equation and sinhGordon equation, Landau-Ginzburg-Higgs equation, Duffing equation, nonlinear telegraph equation are the special cases of the nonlinear wave equation presented in this paper.

几个有重要应用的非线性数学物理方程,如矿方程,Klein-Gordon方程,Sine-Gordon方程,及Sinh-Gordon方程的近似,Landau-Ginzburg-Higgs方程,Duffing方程,非线性电报方程等都可作为该方程的特殊情形得到相应的显式精确解,这里方法也可推广到n+1维空间情形。

Chapter 2 is devoted to study of exact solutions of the nonlinear evolution equations. Using solutions of a Bernoulli equation instead of tanh in tanh-function method we find some more general solutions of the KdV-Burgers-Kuramoto equation , and by using the nonlinear telegraph equation we show that there are many different choices on its balancing number m and the power n of the nonlinear term in Bernoulli equation by which we can recover the previously known solutions and also can derive new square root type solitary wave solutions. Exact solitary wave solutions for a surface wave equation are obtained by means of the homogeneous balance method. We also present an approach for constructing the solitary wave solutions and non-solitary wave solutions of the nonlinear evolution equations by using the homogeneous balance method directly, which is also used to find the steady state solutions, solitary wave solutions and the non-solitary wave solutions of the 2+1 dimensional dispersive long wave equations. The soliton-like solutions of the BLMP equation and the 2+1 dimensional breaking soliton equation are found by use of the symbolic-computation-based Method.

第二章中研究了非线性发展方程的精确解:用双曲正切函数法中的双曲正切函数换为Bernoulli方程的解的方法而给出KdV-Burgers-Kuramoto方程的精确解并用非线性电波方程为例说明了平衡数m和Bernoulli方程中非线性项的次数n有着多种选择的可能,它不但使我们能找到已知解而且也能找出新的根式孤立波解;用齐次平衡法给出一个曲面波方程的精确孤立波解,并提出直接用齐次平衡法寻找非线性发展方程的孤立波解、非孤立波解的方法,作为应用给出2+1维色散长波方程组等的定态解、孤立波解、非孤立波解等;用Symbolic-computation-basedMethod获得BLMP方程和2+1维破裂孤子方程的类孤子解;提出sine-Gordon型方程的直接求解方法,并获得sine-Gordon方程、双sine-Gordon方程、sinh-Gordon方程、MKdV-sine-Gordon方程和Born-Infeld方程等的精确孤立波解。

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