本文選題：薛定諤方程 + 雙線性�。� 參考：《華北電力大學(xué)(北京)》2017年碩士論文

【摘要】：非線性發(fā)展方程可以描述等離子體、流體力學(xué)、非線性光學(xué)等自然現(xiàn)象。本文分別以一個高階非線性薛定諤方程和相應(yīng)的變系數(shù)高階非線性薛定諤方程為數(shù)學(xué)模型,從解的角度對孤立波在非線性系統(tǒng)中傳播的特性進(jìn)行理論研究。研究對象帶有高階奇數(shù)項和偶數(shù)項,其在解釋相關(guān)自然現(xiàn)象的基本規(guī)律時比一般非線性薛定諤方程更準(zhǔn)確。首先,本文通過雙線性的方法得到單孤子解和二孤子解,并且研究了高階項對孤子解的影響和兩孤子之間的相互作用。其次,根據(jù)廣義的達(dá)布變換,我們獲得了方程的呼吸子解和怪波解。通過選取不同的譜參數(shù)討論了二階呼吸子的動力學(xué)性質(zhì),同時也研究了呼吸子和怪波之間的碰撞。最后,文章以高階非線性薛定諤方程的解為基礎(chǔ),構(gòu)造出了非均勻高階非線性薛定諤方程的精確解。
[Abstract]:Nonlinear evolution equations can describe natural phenomena such as plasma hydrodynamics nonlinear optics and so on. In this paper, a higher order nonlinear Schrodinger equation and a corresponding variable coefficient high order nonlinear Schrodinger equation are used as mathematical models to study theoretically the propagation characteristics of solitary waves in nonlinear systems from the point of view of solution. The object of study has higher order odd and even terms, which is more accurate than the general nonlinear Schrodinger equation in explaining the basic laws of related natural phenomena. Firstly, the single soliton solution and the two-soliton solution are obtained by bilinear method, and the influence of higher order terms on the soliton solution and the interaction between the two solitons are studied. Secondly, according to the generalized Darboux transform, we obtain the respiratory subsolutions and odd wave solutions of the equation. The dynamical properties of the second order respiration are discussed by selecting different spectral parameters, and the collision between the respiratory and strange waves is also studied. Finally, based on the solution of the higher order nonlinear Schrodinger equation, the exact solution of the nonuniform high order nonlinear Schrodinger equation is constructed.
【學(xué)位授予單位】：華北電力大學(xué)(北京)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

【參考文獻(xiàn)】

相關(guān)期刊論文 前3條

1 柳偉;邱德勤;賀勁松;;Localized Properties of Rogue Wave for a Higher-Order Nonlinear Schr?dinger Equation[J];Communications in Theoretical Physics;2015年05期

2 郭柏靈;;非線性Schrdinger方程(Ⅰ):Bose-Einstein凝聚和怪波現(xiàn)象[J];數(shù)學(xué)進(jìn)展;2011年04期

3 王明亮,李志斌,周宇斌;齊次平衡原則及其應(yīng)用[J];蘭州大學(xué)學(xué)報;1999年03期

，

本文編號：1864160