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摘要 本文利用推廣的Tanh函數(shù)展開(kāi)法、函數(shù)展開(kāi)法和指數(shù)函數(shù)展開(kāi)法討論了（2+1）維Bogoyavlenskii’s廣義破裂孤子方程，得到了方程的一些精確行波解.這些解的形式可分為四類(lèi)：三角函數(shù)解、雙曲函數(shù)解、指數(shù)函數(shù)解以及有理數(shù)解.利用數(shù)學(xué)軟件Mathematica對(duì)這些精確行波解進(jìn)行了圖像模擬. 關(guān)鍵詞：Bogoyavlenskii’s方程；精確行波解；推廣的Tanh函數(shù)法；函數(shù)法；指數(shù)函數(shù)法.
ABSTRACT In this paper, the general Tanh-function method, expansion method and exponential expansion method are used to discuss Bogoyavlenskii 's general breaking soliton equation. Some exact traveling solutions are obtained, which include trigonometric functions solutions, hyperbolic function solutions, exponential solutions and rational function solutions. The simulated images of them are obtained by Mathematica. Keywords: Bogoyavlenskii 's general breaking soliton equation; Exact travelling wave solutions ; general Tanh function method; expansion method; Exponential expansion method.
目錄 摘要 ABSTRACT 第一章 引言 第二章 利用函數(shù)展開(kāi)法求解Bogoyavlenskii’s方程的精確行波解 2.1 推廣的Tanh函數(shù)展開(kāi)法 2.2 函數(shù)展開(kāi)法 2.3 指數(shù)函數(shù)展開(kāi)法 小結(jié) 參考文獻(xiàn) 致謝
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