發(fā)布時間：2018-02-13 03:29

  本文關(guān)鍵詞： 精確解 李對稱 Tanh方法 最簡函數(shù)法 冪級數(shù)解法 廣義(G　出處：《江蘇大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：目前,非線性科學(xué)研究已經(jīng)成為科學(xué)研究領(lǐng)域的焦點之一。在不同的研究領(lǐng)域中,會遇到各種不同類型的非線性方程,對如何求解這些不同類型的非線性方程也成為了該領(lǐng)域研究的關(guān)鍵。近年來,隨著數(shù)學(xué)機械化的廣泛應(yīng)用,出現(xiàn)了大量的求解非線性方程的新方法,這些方法有效地推動了非線性系統(tǒng)的發(fā)展。本文研究了兩類方程的精確解,即非線性變系數(shù)Sharma-Tasso-Olver(STO)方程和分數(shù)階非線性Klein-Gordon方程。本文共分為五個章節(jié)。第一章,在這一章主要介紹了變系數(shù)非線性方程及分數(shù)階偏微分方程的研究背景以及現(xiàn)有的研究方法等,最后給出了全文各章的研究內(nèi)容。第二章,在這一章首先介紹了STO方程的研究背景以及已有的求解方法和結(jié)果,其次基于李點對稱方法對變系數(shù)STO方程進行對稱分析,得到了其對稱約化方程,最后利用tanh法、最簡函數(shù)法和冪級數(shù)解法得到了所有的約化方程的精確解,進而得到變系數(shù)STO方程的精確解。第三章,利用廣義(G'/G)展開法再次討論了變系數(shù)STO方程,得到了不同于第二章結(jié)果的新的精確解。第四章,在這一章中,利用復(fù)雜變換結(jié)合三種不同的方法得到了改進的Riemann-Liouville分數(shù)階非線性Klein-Gordon方程的精確解。第五章,對全文進行總結(jié)。
[Abstract]:At present, nonlinear scientific research has become one of the focuses of scientific research. In different research fields, there are various types of nonlinear equations. In recent years, with the wide application of mathematical mechanization, a large number of new methods for solving nonlinear equations have emerged. These methods have effectively promoted the development of nonlinear systems. In this paper, we study the exact solutions of two kinds of equations, namely, Sharma-Tasso-Olversto equation and fractional nonlinear Klein-Gordon equation. This paper is divided into five chapters. In this chapter, the research background and existing research methods of variable coefficient nonlinear equations and fractional partial differential equations are introduced. In this chapter, the research background of STO equation, the existing methods and results are introduced. Secondly, based on the lie point symmetry method, the symmetric reduction equation of STO equation with variable coefficients is obtained. Finally, the tanh method is used. The exact solutions of all the reduced equations are obtained by the simplest function method and the power series method, and then the exact solutions of the variable coefficient STO equation are obtained. In chapter 3, the STO equation with variable coefficients is discussed again by using the generalized GG / G expansion method. In this chapter, the exact solutions of the improved Riemann-Liouville fractional order nonlinear Klein-Gordon equation are obtained by using complex transformation combined with three different methods. Chapter 5th summarizes the full text.
【學(xué)位授予單位】：江蘇大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175.29

【參考文獻】

相關(guān)期刊論文 前1條

1 范恩貴,張鴻慶;非線性孤子方程的齊次平衡法[J];物理學(xué)報;1998年03期

，

本文編號：1507225