發(fā)布時(shí)間：2018-07-11 22:03

  本文選題：對(duì)稱約化 + 破裂孤子方程　； 參考：《北方民族大學(xué)》2017年碩士論文

【摘要】：本文主要研究了幾類非線性微分方程的對(duì)稱分析�；诜�(hào)計(jì)算軟件Maple,本文利用樓直接方法研究了一個(gè)(2+1)-維Toda-like晶格方程的對(duì)稱變換。并基于求得的對(duì)稱變換,得到了這個(gè)微分差分方程一個(gè)新的類孤子解,并給出數(shù)值算例。同時(shí)利用經(jīng)典李群法對(duì)(2+1)-維非等譜破裂孤子方程組以及它的Lax對(duì)進(jìn)行對(duì)稱約化,并假設(shè)譜參數(shù)為一個(gè)額外的場(chǎng),得到新的約化方程和Lax對(duì),通過比較約化后的方程和約化后的Lax對(duì)的相容條件,我們發(fā)現(xiàn)約化的Lax對(duì)恰好是約化方程的Lax對(duì),并通過一個(gè)約化后的Lax對(duì)求得了原方程的精確解。本論文的結(jié)構(gòu)如下:引言部分介紹了可積系統(tǒng)和孤子理論的歷史背景和發(fā)展?fàn)顩r,并且闡述了非線性微分方程的求解方法和對(duì)稱分析,同時(shí)介紹了可積系統(tǒng)的理論背景及其廣泛應(yīng)用。第二、三章是文章的主要內(nèi)容。最后對(duì)整篇文章進(jìn)行總結(jié)。
[Abstract]:In this paper, the symmetry analysis of several nonlinear differential equations is studied. Based on the symbolic computing software Maple. the symmetric transformation of a (21) -dimensional Toda-like lattice equation is studied by building direct method. Based on the obtained symmetry transformation, a new soliton-like solution of the differential difference equation is obtained, and a numerical example is given. At the same time, the classical Li Qun method is used to symmetrically reduce (21) -dimensional nonisospectral rupture soliton equations and its lax pairs. The spectral parameters are assumed to be an extra field, and a new reductive equation and lax pair are obtained. By comparing the compatibility conditions between the reduced equation and the reduced lax pair, we find that the reduced lax pair is exactly the lax pair of the reduced equation, and the exact solution of the original equation is obtained by a reduced lax pair. The structure of this paper is as follows: the introduction introduces the historical background and development of the integrable system and soliton theory, and expounds the methods of solving nonlinear differential equations and symmetry analysis. At the same time, the theoretical background of integrable system and its wide application are introduced. The second, third chapter is the main content of the article. Finally, the article is summarized.
【學(xué)位授予單位】：北方民族大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175

【參考文獻(xiàn)】

相關(guān)期刊論文 前5條

1 ;Clarkson-Kruskal Direct Similarity Approach for Differential-Difference Equations[J];Communications in Theoretical Physics;2005年12期

2 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(bào);1998年03期

3 曾云波，李翊神;THE　GENERAL　SCHEME　FOR　HIGHER－ORDER　DECOMPOSITIONS　OF　ZERO－CURVATURE　EQUATIONS　ASSOCIATED　WITH■（2）[J];Acta Mathematicae Applicatae Sinica(English Series);1996年04期

4 陳登遠(yuǎn)，朱寧生，朱敏;KP系統(tǒng)的對(duì)稱約束[J];數(shù)學(xué)物理學(xué)報(bào);1996年01期

5 屠規(guī)彰;一族新的可積系及其Hamilton結(jié)構(gòu)[J];中國科學(xué)(A輯 數(shù)學(xué) 物理學(xué) 天文學(xué) 技術(shù)科學(xué));1988年12期

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