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.
Using the painleve method of singularity analysis , two integras of motion of the reduced three - wave interaction system were found )奇异分析法，已经找到了约化的三波相互作用系统的两个运动积分。
3.
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。
4.
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
