kaup 中文意思是什麼

Integrable decomposition of the multicomponent kaup - newell equation

方程的一個可積分解

New multisoliton solutions forwhitham - broer - kaup equations in shallow water

淺水波方程新的多孤子解

The mostly conclusion of this part is as follows, on the conditon of travelling wave, the exact solitary wave solutions to some nonlinear wave equations such as sawada - kotera equation, kaup - kupershmidt equation, the fifth order kdv equation, fisher - kolmogorov equation, on the help of the computer algebraic system ( maple ), are explicitly established by making use of the hyperbolic function method. this part is maken up of three sections

本部分的主要結論如下，利用雙曲函數展開法，在行波條件下，對sawada - kotera方程， kaup - kupershmidt方程，五階kdv方程， fisher - kolmogorov方程，等幾類非線性波動方程求解，將其孤立波表示為雙曲函數的多項式，從而將非線性波方程的求解問題轉化為非線性代數方程組的求解問題，並藉助于計算機代數系統求解非線性代數方程組，最終獲得了這些非線性波動方程的若干精確孤立波解。

( 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。

Burgers equation and whitham - broer - kaup shallow water equations are chosen to illustrate this method

Burgers方程和whitham ? broer ? kaup淺水波方程組為例來說明這一方法。

The tu ' s scheme is extended to the generalized dirac spectral problem with an arbitrary function, the generalized kaup - newell spectral problem and the new 3x3 spectral problem with five potentials such that their lax integrabie integrabie hierarchies of equations and liouville integrabie hamilton structures are obtained. chapter 7 is devote to higher - order constraint flow, involutive system, lax representation, r - matrix and the separation of variables

第六章研究了lax可積的新的方程族和liouville可積的n - hamilton結構方面的問題：將屠格式推廣到新的含有任意函數的廣義dirac族的譜問題、廣義kaup - newell譜問題及含有五個位勢函數的3 3譜問題，研究了它們的lax可積的方程族和liouville可積的hamilton結構。

Generalized dromion structures of the higher order dimensional broer - kaup equations

方程的多孤子解結構

New exact solutions for - dimensional broer - kaup - kupershmidt equations

色散長波方程和變形色散水波方程特殊形狀的多孤子解

In the chapter 3, the author brings many new solutions of the broer - kaup ( bk ) equation in ( 2 + 1 ) - dimensional space and kp equation by using new transformation developed by doc. yan

在第三章中，作者利用閆振亞博士提出的推廣的riccati方程變換方法，解決了（ 2 + 1 ）維bk方程，和廣義的kp方程的求解問題，得到了許多具有物理意義的新解。