推进方式的参考Jacobian网格优化方法

将参考Jacobian方法与前沿推进方法相结合,设计一种推进方式的参考Jacobian网格优化方法.该方法从计算区域的部分边界开始,沿着给定的方向逐步推进,每前进一步都以相邻的两行(或两列)结点为边界采用参考Jacobian方法进行优化,其中处于后方的一行(或一列)使用的是前一步优化后的结点.分析及数值实验表明,与参考Jacobian方法相比,不仅能大幅度降低执行时间,而且优化后的网格在几何品质方面相当接近,甚至更优,得到的网格与Lagrange网格更接近.     

Exact Jacobian Elliptic Function Solutions to sinh-Gordon Equation

In this paper, two transformations are introduced to solve sinh-Gordon equation by using the knowledge of elliptic equation and Jacobian elliptic functions. It is shown that different transformations are required in order to obtain more kinds of solutions to the sinh-Gordon equation.     

Jacobian Elliptic Function Method and Solitary Wave Solutions for Hybrid Lattice Equation

In this paper, we have successfully extended the Jacobian elliptic function expansion approach to nonlinear differential-difference equations. The Hybrid lattice equation is chosen to illustrate this approach. As a consequence, twelve families of Jacobian elliptic function solutions with different parameters of the Hybrid lattice equation are obtained. When the modulus m→1 or 0, doubly-periodic solutions degenerate to solitonic solutions and trigonometric function solutions, respectively.     

Exact Jacobian Elliptic Function Solutions to sine-Gordon Equation

In this paper, four transformations are introduced to solve single sine-Gordon equation by using the knowledge of elliptic equation and Jacobian elliptic functions. It is shown that different transformations are required in order to obtain more kinds of solutions to the single sine-Gordon equation.     

Exact Jacobian Elliptic Function Solutions to sine-Gordon Equation

In this paper, four transformations are introduced to solve single sine-Gordon equation by using the knowledge of elliptic equation and Jacobian elliptic functions. It is shown that different transformations are required in order to obtain more kinds of solutions to the single sine-Gordon equation.     

非线性振动、非线性波与Jacobi椭圆函数(续)

5　正弦戈登方程、扭结、反扭结波、呼吸孤立波正弦戈登方程 (sing -Gordon方程 ,简记为SG方程 )φxx- φtt=sin φ (38)是自然科学和应用科学中出现的另一个重要的非线性发展方程 (演化方程 ) .在晶体位错的传播、磁旋波在铁磁材料中的传播、约瑟夫森 (Josephson)结中继传输线等乃至生物物理的诸多问题中都应用了这一方程 .本文从单摆弹簧链模型这一特例引入SG方程 .考虑如图 3所示的N个相连弹簧 -单摆运动方程 (称为单摆弹簧链 ) .N个单摆悬挂在横置的诸弹簧上 ,每个摆的长度和质量均相同 ,每个螺旋弹簧的长度和劲度系数也相同 ,则第i…     

Some New Exact Solutions of Jacobian Elliptic Function of Petviashvili Equation

By using the modified mapping method, we find new exact solutions of the Petviashvili equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions.     

New Jacobian Elliptic Function Solutions of Modified KdV Equation: Ⅱ

Recently, we obtained thirteen families of Jacobian elliptic function solutions of mKdV equation by usingour extended Jacobian elliptic function expansion method. In this note, the mKdV equation is investigated and anotherthree families of new doubly periodic solutions (Jacobian elliptic function solutions) are fbund again by using a newtransformation, which and our extended Jacobian elliptic function expansion method form a new method still called theextended Jacobian elliptic function expansion method. The new method can be more powertul to be applied to othernonlinear differential equations.     

New Jacobian Elliptic Function Solutions of Modified KdV Equation: Ⅲ

More recently, sixteen families of Jacobian elliptic function solutions of mKdV equation have been foundby using our extended Jacobian elliptic function expansion method. In this paper, we continue to improve our methodby using another eight pairs of the closed Jacobian elliptic functions. The mKdV equation is chosen to illustrate theimproved method such that another eight families of new Jacobian elliptic function solutions are obtained again. Thenew method can be more powerful to be applied to other nonlinear differential equations.     

The moduli space of flat SU (2) and SO (3) connections over surfaces

All the connected components of the moduli space of flat connections on SU (2) and SO (3) (trivial and non-trivial) bundles over closed oriented surfaces are determined. The symplectic structure and volumes of the non-maximal strata of the moduli space are also determined.     

New Jacobian Elliptic Function Solutions of Modified KdV Equation: II

Recently, we obtained thirteen families of Jacobian elliptic function solutions of mKdV equation by using our extended Jacobian elliptic function expansion method. In this note, the mKdV equation is investigated and another three families of new doubly periodic solutions (Jacobian elliptic function solutions) are found again by using a new transformation, which and our extended Jacobian elliptic function expansion method form a new method still called the extended Jacobian elliptic function expansion method. The new method can be more powerful to be applied to other nonlinear differential equations.     

Hidden symmetry of hyperbolic monopole motion

Hyperbolic monopole motion is studied for well separated monopoles. It is shown that the motion of a hyperbolic monopole in the presence of one or more fixed monopoles is equivalent to geodesic motion on a particular submanifold of the full moduli space. The metric on this submanifold is found to be a generalisation of the multi-centre Taub-NUT metric introduced by LeBrun. The one centre case is analysed in detail as a special case of a class of systems admitting a conserved Runge–Lenz vector. The two centre problem is also considered. An integrable classical string motion is exhibited.     

General Jacobian elliptic function expansion method and its applications

An extended Jacobian elliptic function expansion method is presented and successfully applied to the nonlinear Schr?dinger (NLS) equation and Zakharov equation. We obtain some new solutions besides Fu et al's results. The results show that our method is more powerful to construct Jacobian elliptic function and can be applied to other nonlinear physics systems.     

New Jacobian Elliptic Function Solutions to Modified KdV Equation: Ⅰ

An extended Jacobian elliptic function expansion method presented recently by us is applied to the mKdVequation such that thirteen families of Jacobian elliptic function solutions including both new solutions and Fu‘s allresults are obtained. When the modulus m → 1 or 0, we can find the corresponding six solitary wave solutions and sixtrigonometric function solutions. This shows that our method is more powerful to construct more exact Jacobian ellipticfunction solutions and can be applied to other nonlinear differential equations.     

Employment of Jacobian elliptic functions for solving problems in nonlinear dynamics of microtubules

We show how Jacobian elliptic functions （JEFs） can be used to solve ordinary differential equations （ODEs） describing the nonlinear dynamics of microtubules （MTs）. We demonstrate that only one of the JEFs can be used while the remaining two do not represent the solutions of the crucial differential equation. We show that a kinkbtype soliton moves along MTs. Besides this solution, we also discuss a few more solutions that may or may not have physical meanings. Finally, we show what kind of ODE can be solved by using JEFs.     

用推广的Jacobian椭圆函数方法解离散的mKdV格子

本文用推广的Jacobian椭圆函数方法求解了离散的mKdV格子，得到了Jacobian椭圆函数双周期解，当模取1时，可得到钟型孤波解和冲击型孤波解。     

一般变换下双Jacobi椭圆函数展开法及应用

将行波变换下修正的双Jacobi椭圆函数展开法推广到范围广泛的一般函数变换下进行.利用这一方法求得了一类非线性方程更多新的周期解，这些解包括了在行波变换下所求得的周期解. 关键词： Jacobi椭圆函数展开法 非线性发展方程 函数变换 周期解     

New Jacobian Elliptic Function Solutions to Modified KdV Equation: I

An extended Jacobian elliptic function expansion method presented recently by us is applied to the mKdV equation such that thirteen families of Jacobian elliptic function solutions including both new solutions and Fu's all results are obtained. When the modulus m→1 or 0, we can find the corresponding six solitary wave solutions and six trigonometric function solutions. This shows that our method is more powerful to construct more exact Jacobian elliptic function solutions and can be applied to other nonlinear differential equations.     

Formal Deformations,Contractions and Moduli Spaces of Lie Algebras

Jump deformations and contractions of Lie algebras are inverse concepts, but the approaches to their computations are quite different. In this paper, we contrast the two approaches, showing how to compute the jump deformations from the miniversal deformation of a Lie algebra, and thus arrive at the contractions. We also compute contractions directly. We use the moduli spaces of real 3-dimensional and complex 3 and 4-dimensional Lie algebras as models for explaining a deformation theory approach to computation of contractions. The research of the authors was partially supported by grants from the Mathematisches Forschungsinstitut Oberwolfach, OTKA T043641, T043034 and the University of Wisconsin-Eau Claire.