计算机非线性发展,非线性发展方程求解的分析.pdf

北京邮电丈学硕士研究生论文

程；齐次平衡法；推广的tanh函数法；经典Lie群方法。

北京邮电大学硕士研究生论文

THESTUDYoFNONLINEAREVoLUTION

ANDSOLUTIONS

EQUATIONS

ABSTRACT

In naturalsciencelikethefluid

many dynamics，biology,

and have

mathematics，plasmaphysits，opticscommunication，solitons

beenwellstudiedand have

widelyapplied，whichimportantpar7sics

this focusonsomesolitonsolutionsofthe

significance．In

paper,we

nonlinear

evolution mainresultsare

equations(N-LEEs)．Thebriefly

statedbelow：

newexact

First，some solutions(soliton-like

solutions the variablecoefficientGL

etc．)ofgeneralized equation,

dark-soliton·likesolutionstitle

including investigated．By

bright-and

adirectansiitzintothe variablecoefficientGL

putting generalized

obtainitssomenewexact solutions，

equation,we solutions(soliton-like

solutions anddiscussthe

similarity etc．)，subsequently,weanalyze

and ofthoseexactsolutions．

propertiespeculiarities

011 the

Second，We

go investigatinggeneralizedcomplexGL(cGL)

withvariable-coefficient．Invirtueofa

equation transformation，

special

thecGL canbetranslatedintosomeknownclassical

equation equations

withsomeconstraintsaboutthevari