Burgers方程的非局域?qū)ΨQ的局域化及對稱約化
發(fā)布時間：2018-11-21 15:06
【摘要】：本文以對稱方法為基本工具,圍繞著對稱的基本理論,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。第一章簡要介紹了對稱的發(fā)展背景和研究現(xiàn)狀,對本文相關(guān)的概念做了解釋和說明,同時概括了本文的主要研究內(nèi)容,并給出1+1維Burgers方程的李點對稱及其群不變解。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)截斷潘勒衛(wèi)展開法得到了Schwarz形式的Burgers方程并構(gòu)造出Burgers方程的非局域?qū)ΨQ,利用非局域?qū)ΨQ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行了推廣,根據(jù)截斷潘勒衛(wèi)展開法得到了Schwarz形式的Bu-rgers方程并構(gòu)造出無窮多非局域?qū)ΨQ,考慮到復(fù)雜性我們先研究n=2的非局域?qū)ΨQ的情況,利用非局域?qū)ΨQ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)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175
本文編號：2347328
[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)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175
【參考文獻】
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
，本文編號：2347328
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