darboux 中文意思是什麼

And based on this conclusion, darboux theorem on open interval is also given

在此基礎上給出有限開區間上的達布定理。

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。

By using darboux transformations, we give the explicit construction for local isometric immer

Gk （ q勺是具有有限uniton數的調和映射

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

An n - fold darboux transformation with multi - parameters for coupled nonlinear evolution equation of multi - component hierarchy is set up with the help of a gauge transformation of the spectral problem, from which the exact solutions of the nonlinear equations are given

摘要利用等譜問題的規范變換，為一對耦合的非線性演化方程建立了一個具有多個參數的n -波達布變換，進而求出了該方程的精確解。

( 1 ) based on two types of riccati equations, two kinds of new methods are proposed to obtain solutions of nonlinear differential equations. twelve families of exact solutions of wbk equation are found by using one of two methods ; ( 2 ) the homogeneous balance method is improved cind investigated to ( 2 + l ) - dimensional broer - kaup equation such that many families of new solutions are derived. ( 4 ) based on the isospectral lax pair of riccati form for generalized kdv equation with the force term, new darboux transformation and solitary - like wave solutions and rational solutions are obtained ; ( 4 ) by constructing darboux transformation and the superposition formula of generalized variable coefficients kdv equation with the force term, new single solitary - like wave solutions, double solitary - like wave solutions and rational solutions are found for ( 2 + l ) - dimensional generalized kp equation

第二章和第三章考慮非線性偏微分方程的精確解的構造：首先給出了c - d對和c - d可積系統的基本理論，然後在第三章中具體研究了它們的應用： （ 1 ）基於兩種riccati方程，提出了兩種新的求解非線性微分方程更多解的方法，利用其中的一種方法，得到了wbk方程的12組精確解； （ 2 ）對齊次子衡法進行改進，以致於獲得了（ 2 + 1 ） -維broer - kaup方程的很多新解； （ 3 ）基於帶有外力項的廣義kdv方程的riccati形式的非等譜lax對，提出了該方程的一個新的darboux變換，利用該變換，得到了新的類孤波解和有理解； （ 4 ）通過構造了帶有外力項的變系數kdv方程的darboux變換及疊加原理，獲得（ 2 + 1 ） -維廣義kp方程的新的類單孤波解、雙類孤波解和有理解。

Asymptotic behavior of global solution for nonlinear generalized euler - poisson - darboux equation

方程整體解的漸近性質

Darboux transformation and explicit solutions of a hierarchy of new discrete soliton equations

一類新離散孤子方程的達布變換與精確解

Darboux ' s theorem

達布定理

The integrability theory was improved substantively by darboux at the end of 19th century

可積性理論的一個實質性改進是由darboux於19世紀末完成的。

For a special case of such a system equation, we derive the exact soliton solutions using the darboux transformation

運用darboux變換求得了該系統的精確解（包括n -孤子解及2 -孤子解） 。

The results are proved by directly solving hnls equation numerically. 2 ) under the nonvanishing boundary, we solve the hirota equation by using darboux transformation

2 ）在非零種子條件下，運用darboux變換，同樣在hirota條件下求解了高階非線性薛定諤（ hnls ）方程。

By using the darboux method of integrability to some ordinary differential equations, under some given parameters conditions, a lot of integrals of motion have been found

在給定參數的條件下，對一些常微分方程，使用經典的darboux變換理論，能夠發現許多運動積分。應用painlev （

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。

The main results are as follows : 1 ) by using akns formalism we construct the lax pair for hirota equation, a higher order nonlinear schroedinger ( hnls ) equation. and based on the lax pair, we present exact n - soliton solution by employing simple, straightforward darboux transformation

其主要結果如下： 1 ）通過運用akns技巧構造了高階非線性薛定諤（ hnls ）方程在hirota可積條件下的拉克斯（ lax ）對，在此基礎上，運用達布變換（ darboux ）給出該方程的n -孤子解。

2. the exact n - soliton solutions of the nonlinear schrodinger equation with time - dependent linear potential are presented by employing the darboux transformation method. as the special cases, bright soliton - solutions are obtained in bose - einstein condensates, and their properties and interaction between solitons are discussed as well

利用darboux變換，對含時線性勢的非線性薛定諤方程進行求解，並研究在耦合外場作用下，準一維玻色-愛因斯坦凝聚體中亮孤子的動力學行為。