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Approximate homotopy similarity reduction for the generalized Kawahara equation via Lie symmetry method and direct method

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Chinese Physics B 2010年第8期19卷 28-34页

作者：刘希忠 Department of Physics Shanghai Jiao Tong University

This paper studies the generalized Kawahara equation in terms of the approximate homotopy symmetry method and the approximate homotopy direct method. Using both methods it obtains the similarity reduction solutions and similarity reduction equations of different orders, showing that the approximate homotopy direct method yields more general approximate similarity reductions than the approximate homotopy symmetry method. The homotopy series solutions to the generalized Kawahara equation are consequently derived.

关键词： approximate homotopy symmetry method approximate homotopy direct method generalized Kawahara equation homotopy series solutions

BB肥和“九二○”对水稻亲本繁殖产量影响的研究

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BB肥和“九二○”对水稻亲本繁殖产量影响的研究

作者：刘希忠西南大学

学位级别：硕士

本文通过田间试验设计的方法,以Ⅱ-32A（不育系）和Ⅱ-32B（保持系）为试验材料,分别采用5种施肥量和3种“九二○”喷施方法进行处理,研究了水稻专用BB肥不同施用量和“九二○”施用时期对三系杂交水稻不育系繁殖产量的影响。主要结果如... 详细信息

本文通过田间试验设计的方法,以Ⅱ-32A（不育系）和Ⅱ-32B（保持系）为试验材料,分别采用5种施肥量和3种“九二○”喷施方法进行处理,研究了水稻专用BB肥不同施用量和“九二○”施用时期对三系杂交水稻不育系繁殖产量的影响。主要结果如下: 1.BB肥对杂交水稻制种不育系产量的影响十分明显,实验证明杂交水稻不育系繁殖与制种应用BB肥做为底肥一次施入,可做为大田繁殖制种的施肥方式之一,以后可以大面积推广。在10—40kg/667m~2水稻专用BB肥施用范围内,随着BB肥施用量的增加,Ⅱ-32A不育系的产量也随之增加其中以施用BB肥为40kg/667m~2产量最高,但BB肥用量超过40kg/667m~2时,制种产量反而下降。因此,BB肥用量过高、过低都会使产量降低。本试验最佳BB肥使用量BB肥40kg/667m~2。 2.使用BB肥,能有效促进群体的增长,茎蘖数增多,高峰苗苗数多,最后有效穗较多。在生产实践中,应该根据田块的具体肥力条件,因地制宜的确定施肥方案。 3.BB肥对上部3片叶子的长、宽和面积影响不显著,但能有效延长花时、花期,并增加母本的柱头外露率,提高受精结实,从而能有效提高制种产量。 4.从九二○的使用效果看,“九二○”能明显提高倒1、2和3节间的长度,对上部3片叶子的长、宽度和面积影响不明显,利于母本授粉,对提高制种结实率和产量有重要效果。在母本出穗5%时,喷施“九二○”5g/667m~2,出穗20%时喷施“九二○”15g/667m~2和在母本出穗20%时一次性喷施“九二○”20g/667m~2的综合效果比出穗30%时一次性喷施“九二○”20g/667m~2的综合效果差,但前两种处理比对照CK明显好。因此,在生产上以母本出穗30%,一次性喷施“九二○”20g/667m~2对提高Ⅱ-32A不育系繁殖产量有明显作用。

关键词：杂交水稻亲本繁殖产量 BB肥 “九二○” 异交结实

Minkowski四维时空M4的主要性质及粒子的相对论运动方程

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Minkowski四维时空M4的主要性质及粒子的相对论运动方程

作者：刘希忠华东师范大学

学位级别：硕士

本文由两部分组成,首先将引入Minkowski向量空间V,V被赋予一个非退化的内积,而且这一内积并非恒为正,因此关于向量长度,及两向量之间的夹角等概念就没有意义了。第一部分介绍Minkowski四维时空中直线与直线及直线和M子流形的位置关系,... 详细信息

本文由两部分组成,首先将引入Minkowski向量空间V,V被赋予一个非退化的内积,而且这一内积并非恒为正,因此关于向量长度,及两向量之间的夹角等概念就没有意义了。第一部分介绍Minkowski四维时空中直线与直线及直线和M子流形的位置关系,特别突出分离函数在其中的作用。第二部分将首先建立在M中运动粒子的相对论性方程并与牛顿的经典运动方程相比较,进而给出动能、质量等概念的相对论表达式。

关键词： Minkowski四维时空分离函数运动粒子的相对论性方程

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初中物理教学中的情感培养

中学物理（初中版） 2009年第11期24卷 38-39页

作者：刘希忠山东省高唐县固河中学

积极的情感能提高学生的生理和心理活动，从而提高教学的效率和质量．那么，在物理教学中如何培养学生的情感呢？

关键词：初中物理教学情感培养心理活动学生

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Communications in Theoretical Physics 2010年第11期54卷 797-802页

作者：刘希忠 Department of Physics Shanghai Jiao Tong University

The perturbed Kaup-Kupershmidt equation is investigated in terms of the approximate symmetry perturbationmethod and the approximate direct method.The similarity reduction solutions of different orders are obtainedfor both methods, series reduction solutions are consequently derived.Higher order similarity reduction equations arelinear variable coefficients ordinary differential equations.By comparison, it is find that the results generated from theapproximate direct method are more general than the results generated from the approximate symmetry perturbationmethod.

关键词： Kupershmidt方程 Lie对称性相似扰动直接法线性常微分方程求解近似方法

Explicit solutions from residual symmetry of the Boussinesq equation

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Chinese Physics B 2015年第3期24卷 19-25页

作者：刘希忠俞军任博 Institute of Nonlinear Science Shaoxing University

The Bcklund transformation related symmetry is nonlocal, which is hard to be applied in constructing solutions for nonlinear equations. In this paper, the residual symmetry of the Boussinesq equation is localized to Lie point symmetry by introducing multiple new variables. By applying the general Lie point method, two main results are obtained： a new type of Backlund transformation is derived, from which new solutions can be generated from old ones; the similarity reduction solutions as well as corresponding reduction equations are found. The localization procedure provides an effective way to investigate interaction solutions between nonlinear waves and solitons.

关键词： Boussinesq equation,localization procedure,residual symmetry,symmetry reduction solution

Approximate Homotopy Symmetry Reduction Method:Infinite Series Reductions to Kawahara Equation

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Communications in Theoretical Physics 2010年第7期54卷 31-34页

作者：刘希忠 Department of Physics Shanghai Jiao Tong University

The Kawahara equation is studied through the approximate homotopy symmetry method.Under thismethod we get the similarity reduction solutions of the Kawahara equation,leading to the corresponding homotopyseries solutions.Furthermore,the similarity solutions of the corresponding reduced linear ordinary differential equationsare aiso considered.

关键词：线性常微分方程同伦方法对称相似约化相似性解

A nonlocal Boussinesq equation:Multiple-soliton solutions and symmetry analysis

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Chinese Physics B 2022年第5期31卷 83-87页

作者：刘希忠俞军 Institute of Nonlinear Science Shaoxing UniversityShaoxing 312000China

A nonlocal Boussinesq equation is deduced from the local one by using consistent correlated bang method.To study various exact solutions of the nonlocal Boussinesq equation,it is converted into two local equations which contain the local Boussinesq equation.From the N-soliton solutions of the local Boussinesq equation,the N-soliton solutions of the nonlocal Boussinesq equation are obtained,among which the(N=2,3,4)-soliton solutions are analyzed with graphs.Some periodic and traveling solutions of the nonlocal Boussinesq equation are derived directly from the known solutions of the local Boussinesq equation.Symmetry reduction solutions of the nonlocal Boussinesq equation are also obtained by using the classical Lie symmetry method.

关键词： nonlocal Boussinesq equation N-soliton solution periodic waves symmetry reduction solutions

New solutions from nonlocal symmetry of the generalized fifth order KdV equation

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Chinese Physics B 2015年第8期24卷 137-141页

作者：刘希忠俞军任博 Institute of Nonlinear Science Shaoxing University

The nonlocal symmetry of the generalized fifth order KdV equation(FOKdV) is first obtained by using the related Lax pair and then localizing it in a new enlarged system by introducing some new variables. On this basis, new Ba¨cklund transformation is obtained through Lie’s first theorem. Furthermore, the general form of Lie point symmetry for the enlarged FOKdV system is found and new interaction solutions for the generalized FOKdV equation are explored by using a symmetry reduction method.

关键词： generalized fifth order Kd V equation,localization procedure,nonlocal symmetry,symmetry reduction solution