發(fā)布時(shí)間：2018-06-20 22:41

  本文選題：多分量CH類型方程 + 尖峰孤子解��； 參考：《內(nèi)蒙古師范大學(xué)》2017年碩士論文

【摘要】：Camassa-Holm(CH)方程有許多獨(dú)特的數(shù)學(xué)性質(zhì)和廣泛的物理意義.CH方程的解及其性質(zhì)的研究極大地豐富了潛水波理論和孤立子理論,這吸引著專家學(xué)者的廣泛關(guān)注.最近,人們將CH方程拓展到耦合多分量的情形,并進(jìn)行大批的研究.求解方程的尖峰孤子解與扭結(jié)型解并分析其動(dòng)態(tài)行為是非線性方程理論的一個(gè)重要方面,本文將主要研究耦合多分量的CH類型方程的多重尖峰孤解子與扭結(jié)型解.第一章介紹了淺水波理論的研究背景、研究現(xiàn)狀及其意義.第二章得到了幾個(gè)多分量CH類型方程的尖峰孤子解,重點(diǎn)研究了二重尖峰孤子解并通過(guò)圖形對(duì)其動(dòng)態(tài)行為進(jìn)行了簡(jiǎn)單分析.第三章研究了可積意義下耦合的二分量CH類型方程,并在不同的參數(shù)條件下,得到了多重扭結(jié)型解.最后,對(duì)全文進(jìn)行了總結(jié),并做了進(jìn)一步展望.
[Abstract]:Camassa-Holmschach equation has many unique mathematical properties and extensive physical meaning. The research on the solution and properties of the Ch equation has greatly enriched the theory of submersible wave and soliton theory, which has attracted extensive attention of experts and scholars. Recently, the Ch equation has been extended to the coupled multicomponent case, and a large number of studies have been carried out. In this paper, we will study the multi-spike soliton solution and the kink type solution of the coupled multi-component Ch type equation, and analyze their dynamic behavior in an important aspect of the theory of nonlinear equations. The first chapter introduces the research background, research status and significance of shallow water wave theory. In the second chapter, we obtain the peak soliton solutions of several multicomponent Ch type equations, and focus on the double spike soliton solutions. In chapter 3, the coupled two-component Ch type equations in integrable sense are studied, and the multi-kink type solutions are obtained under different parameter conditions. Finally, the full text is summarized, and further prospects are made.
【學(xué)位授予單位】：內(nèi)蒙古師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175.29

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相關(guān)期刊論文 前3條

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本文編號(hào)：2045936