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摘 要:本文利用輔助函數(shù)方法對廣義反應(yīng)Duffing方程進(jìn)行了研究,獲得了一些該方程的周期波解，孤立波解和紐子波解. 本文分為三部分.第一部分介紹了非線性波動方程的研究現(xiàn)狀及意義.第二部分介紹了輔助函數(shù)方法，利用該方法求廣義Duffing方程的精確解.第三部分簡要說明了論文的研究成果. 關(guān)鍵詞：廣義反應(yīng)Duffing方程;輔助函數(shù)方法;Jacobi橢圓函數(shù);精確解;行波
Abstract:In this paper, a general nonlinear Duffing equation is studied by the auxiliary function method, some periodic wave, solitary wave and kink wave solutions, which expressed various functions are obtained. This paper consists of three parts. The present researching situations and significances of Nonlinear wave equations are introduced in the first part. In the second part, the auxiliary function method is introduced and some exact solutions of the generalized nonlinear Duffing equations are obtained by using the method. The research results of the paper are analyzed in the third part. Key words: Duffing equation; Auxiliary function method; Jacobi elliptic function; Exact solution; Travelling wave
目錄 第一章 緒 論-1 1.1非線性波動方程的研究意義及現(xiàn)狀-1 1.2本文的主要研究內(nèi)容-1 第二章 廣義反應(yīng)Duffing方程的精確解-3 2.1 輔助函數(shù)法介紹-3 2.2 Duffing方程的精確解-4 2.2.1當(dāng)滿足方程（5）時，Duffing模型的精確行波解-4 2.2.2當(dāng)滿足方程（6）時，Duffing模型的精確行波解-12 2.2.3當(dāng)滿足方程（7）時，Duffing模型的精確行波解-38 第三章 結(jié) 論-44 參考文獻(xiàn)-45 附 錄 -47 致 謝-49 |
