English translation for "backlund"

巴克隆德
巴克伦

Example Sentences:

	1.	Chapter 4 deals with painleve integrability and backlund transformation 第四章讨论了非线性微分方程的painleve可积性和backlund变换。
	2.	And some exact explicit solutions of burgers equation and sine - gordon equation are obtained through separately constructing their backlund transformations 本文应用这个变换方法分别建立burgers方程和sine - gordon方程的bcklund变换关系，并且得到了一些有意义的精确解析解。
	3.	Upon now , there are several available methods in solving the nlepdes , for example , the inverse scattering transform , the hirota method , the backlund transformation method and the homogeneous method 至今比较成功的系统求解方法有散射反演法， hirota方法， bcklund变换法和齐次平衡法。
	4.	Chapter3 : the method of backlund transformation is introduced . its aim is to build the connection between the solutions of two different equation , or the connection between the solutions of one same equation 第三章介绍bcklund变换法，它是建立不同方程解之间联系，或同一方程不同解之间联系的一种变换方法。
	5.	The symplectic uniton and symplectic extended uniton are introduced . the method of the symplectic backlund transformation and the darboux transformation is used to construct new symplectic uniton from a known one 引进了辛uniton的概念，通过b icklund变换和darboux变换，给出了由已知辛uniton构造新的辛uniton的纯代数方法。
	6.	Two types of ( 2 + l ) - dimensional generalized burgers equations are shown to pass the painleve test by using wtc method , and their backlund transformations are obtained through painleve truncating expansion . cole - hopf transformation is their special case 利用wtc方法证明了两类( 2 + 1 ) -维广义burgers方程是painleve可积的，并经截断展开原理获得了它们的backlund变换，其中cole - hopf变换是其特例。
	7.	In this paper , i consider the traveling wave solutions and peakons of the generalized camassa - holm ( gch ) equation and give the express of the solitons of this equation . the peakons and their figures of the gch equation are given with the mathematic software for m - 1 , m = 2 and m = 3 in particular ; for m = 3 , i get the generalized dissipative camassa - holm equations by adding a dissipative term and find two types exact traveling wave solutions of this equations . i also apply the homogeneous balance method into the gch equation so that i get a group of smooth solutions for m = 2 and m = 3 and the backlund transformation for m - 3 of the gch equation 本文研究广义camassa - holm ( gch )方程的行波孤立子解及尖峰孤立子解，给出gch方程的行波孤立子解的表达式，特别的，对m = 1 、 m = 2 、 m = 3时利用mathematica数学软件进行计算，解出了gch方程的尖峰孤立子解，并给出了此时gch方程的尖峰孤立子解的图形，使数值分析和理论相结合；对m = 3时的gch方程增加一耗散项u _ ( xx )后得到广义耗散camassa - holm方程，并解出此方程的两类精确行波解；本文将齐次平衡法应用到gch方程中，解出m = 2 、 m = 3时的gch方程的一组光滑解，同时应用此方法得到了m = 3时的gch方程的backlund变换。
	8.	In this dissertation , with the aid of many types of constructive transformations and symbolic computation , some topics in nonlinear waves and integrable system are studied , including exact solutions , painleve integrability , backlund transformation , darboux transformation , symmetry ( similarity reduction ) , conditional symmetry , lax integrable hierarchy , liouville integrable n - hamilton structure , constraint flow , involutive system , lax representation , r - matrix , separation of variables and integrable couplings . chapter 2 and 3 are devoted to investigating exact solutions of nonlinear wave equations : firstly , the basic theories of c - d pair and c - d integrable system are presented 本文以构造性的变换及符号计算为工具，来研究非线性波和可积系统中的一些问题：精确解(如孤子解、周期解、有理解、 dromion解及compacton解等) 、 panileve可积性、 backlund变换、 darboux变换、对称(相似约化) 、条件对称、 lax可积族、 liouville可积的n - hamilton结构、约束流、对合系统、 lax表示、 r -矩阵、变量分离及可积的耦合系统
	9.	This paper is to study harmonic maps into symplectic groups and local isometric immersions into space forms by means of the soliton theory . by realizing an action of the rational loop group on the spaces of corrsponding solutions , we get the backlund transformation and the darboux transformation , and thereby we give the explicit construction for harmonic maps into symplectic groups and local isometric immersions into space forms via purely algebraic algorithm 主要用孤立子理论研究到辛群的调和映射和到空间形式的局部等距浸入，通过有理loop群在其解空间上的dressing作用，给出b icklund变换和darboux变换的显式表示，从而获得到辛群及其对称空间的调和映射和到空间形式的局部等距浸入的纯代数构造方法。
	10.	The second part , with the aid of many types constructive transformation and symbolic computation ( especially wu algebraic elemination method ) , some topics in nonlinear evolution equation are studied , including exact solution ( solitary solution , periodic solution , rational function solutions and jacobian function solution ) , backlund transformation , cole - hopf transformation , dromion solution and its construction etc . charter 2 introduces ac = bd model and its application about partial differential equations 第二部分以构造性的变换及符号计算特别是(吴代数消元法)为工具，来研究非线性演化方程中的一些问题：精确解(如孤子解、周期解、有理解和雅可比椭圆函数解(双周期解)等) 、 backlund变换、 hopf变换， dromion解及衰变结构等第二章介绍了求解pdes的ac = bd模式及其在偏微分方程中的作用。

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