darboux equation 中文意思是什麼
darboux equation
解釋
達布方程-
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 -
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。 -
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。
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