【摘要】：本文以對(duì)稱(chēng)方法為基本工具,圍繞著對(duì)稱(chēng)的基本理論,研究了非線性偏微分方程,并給出了貝克隆變換及其新的群不變解。第一章簡(jiǎn)要介紹了對(duì)稱(chēng)的發(fā)展背景和研究現(xiàn)狀,對(duì)本文相關(guān)的概念做了解釋和說(shuō)明,同時(shí)概括了本文的主要研究?jī)?nèi)容,并給出1+1維Burgers方程的李點(diǎn)對(duì)稱(chēng)及其群不變解。第二章利用了潘勒衛(wèi)分析法中的WTC方法證明了Burgers方程是潘勒衛(wèi)可積的。第三章根據(jù)截?cái)嗯死招l(wèi)展開(kāi)法得到了Schwarz形式的Burgers方程并構(gòu)造出Burgers方程的非局域?qū)ΨQ(chēng),利用非局域?qū)ΨQ(chēng)局域化的思想求出自貝克隆變換及群不變解。最后我們將上面的方法進(jìn)行了推廣,根據(jù)截?cái)嗯死招l(wèi)展開(kāi)法得到了Schwarz形式的Bu-rgers方程并構(gòu)造出無(wú)窮多非局域?qū)ΨQ(chēng),考慮到復(fù)雜性我們先研究n=2的非局域?qū)ΨQ(chēng)的情況,利用非局域?qū)ΨQ(chēng)局域化的思想求出自貝克隆變換及群不變解,特別還給出了孤子與Kummer波以及Airy波的新的相互作用解。
[Abstract]:In this paper, the nonlinear partial differential equations are studied by using the symmetric method as a basic tool, and around the basic theory of symmetry, and the Bayclon transformation and its new group invariant solutions are given. The first chapter briefly introduces the development background and research status of symmetry, explains and explains the related concepts in this paper, summarizes the main research contents of this paper, and gives the lie point symmetry and its group invariant solutions of 11-dimensional Burgers equation. In the second chapter, we prove that the Burgers equation is Pandler's integrable by using the WTC method in the Panlerweiss analysis method. In chapter 3, we obtain the Burgers equation in Schwarz form and construct the nonlocal symmetry of the Burgers equation according to the truncated Panlerweiser expansion method. We use the idea of nonlocal symmetry localization to obtain the solution derived from the Beacon transform and group invariant. Finally, we generalize the above method, obtain the Bu-rgers equation in Schwarz form and construct infinite nonlocal symmetries according to the truncated Panlerwey expansion method. Considering the complexity, we first study the case of nonlocal symmetry of NW 2. By using the idea of nonlocal symmetric localization, we obtain the solution derived from the Beacon transform and the group invariant solution. In particular, the new interaction solutions of soliton with Kummer wave and Airy wave are given.
【學(xué)位授予單位】：寧波大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O175

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 金艷;賈曼;樓森岳;;Nonlocalization of Nonlocal Symmetry and Symmetry Reductions of the Burgers Equation[J];Communications in Theoretical Physics;2012年12期

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本文編號(hào)：2347328