backlund 中文意思是什麼

backlund 解釋
巴克隆德
  1. As far as the discussion about the structures is concerned, to some extent, it may be said to be an application to the backlund transformation : fix a solution qn to the system ( l. 3 ), construct a group of solutions qn different from qn through the backlund transformation, and then prove that qn is convergent to qn. in the section 4, it is vital for us to find out the fixed solution n to the equation ( 3. 1 ) in the theorem3. 2, which is completed in the lemma4. 2 and theorem4. 3

    第四節對方程（ 1 . 3 ）的解的性態的討論，在一定程度上也可說是對定理3 . 2的一個應用：給定方程的一個解q _ n ，然後通過貝克朗變換構造了一系列不同於q _ n的解q _ n ，之後證明了q _ n收斂于q _ n 。
  2. 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

    本文研究廣義camassa - holm （ gch ）方程的行波孤立子解及尖峰孤立子解，給出gch方程的行波孤立子解的表達式，特別的，對m = 1 、 m = 2 、 m = 3時利用mathematica數學軟體進行計算，解出了gch方程的尖峰孤立子解，並給出了此時gch方程的尖峰孤立子解的圖形，使數值分析和理論相結合；對m = 3時的gch方程增加一耗散項u _ （ xx ）后得到廣義耗散camassa - holm方程，並解出此方程的兩類精確行波解；本文將齊次平衡法應用到gch方程中，解出m = 2 、 m = 3時的gch方程的一組光滑解，同時應用此方法得到了m = 3時的gch方程的backlund變換。
  3. 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

    主要用孤立子理論研究到辛群的調和映射和到空間形式的局部等距浸入，通過有理loop群在其解空間上的dressing作用，給出b icklund變換和darboux變換的顯式表示，從而獲得到辛群及其對稱空間的調和映射和到空間形式的局部等距浸入的純代數構造方法。
  4. Chapter 4 deals with painleve integrability and backlund transformation

    第四章討論了非線性微分方程的painleve可積性和backlund變換。
  5. 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

    本文以構造性的變換及符號計算為工具，來研究非線性波和可積系統中的一些問題：精確解（如孤子解、周期解、有理解、 dromion解及compacton解等） 、 panileve可積性、 backlund變換、 darboux變換、對稱（相似約化） 、條件對稱、 lax可積族、 liouville可積的n - hamilton結構、約束流、對合系統、 lax表示、 r -矩陣、變量分離及可積的耦合系統
  6. 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

    第二部分以構造性的變換及符號計算特別是（吳代數消元法）為工具，來研究非線性演化方程中的一些問題：精確解（如孤子解、周期解、有理解和雅可比橢圓函數解（雙周期解）等） 、 backlund變換、 hopf變換， dromion解及衰變結構等第二章介紹了求解pdes的ac = bd模式及其在偏微分方程中的作用。
  7. 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

    引進了辛uniton的概念，通過b icklund變換和darboux變換，給出了由已知辛uniton構造新的辛uniton的純代數方法。
  8. And some exact explicit solutions of burgers equation and sine - gordon equation are obtained through separately constructing their backlund transformations

    本文應用這個變換方法分別建立burgers方程和sine - gordon方程的bcklund變換關系，並且得到了一些有意義的精確解析解。
  9. 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

    至今比較成功的系統求解方法有散射反演法， hirota方法， bcklund變換法和齊次平衡法。
  10. 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

    第三章介紹bcklund變換法，它是建立不同方程解之間聯系，或同一方程不同解之間聯系的一種變換方法。
  11. 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方法證明了兩類（ 2 + 1 ） -維廣義burgers方程是painleve可積的，並經截斷展開原理獲得了它們的backlund變換，其中cole - hopf變換是其特例。
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