本文選題：超對稱柱KdV方程 + Hirota雙線性導(dǎo)數(shù)法��； 參考：《華東理工大學(xué)》2017年碩士論文

【摘要】：本文主要研究了超對稱柱KdV方程,將非線性方程求解的三種方法,雙線性導(dǎo)數(shù)法,雙線性Backlund變換,Wronskian技巧推廣到超對稱柱KdV方程中。首先,我們利用直接法將柱KdV方程超對稱化,得到超對稱柱KdV方程。通過適當(dāng)?shù)淖兞孔儞Q,利用雙線性導(dǎo)數(shù)推導(dǎo)出超對稱柱KdV方程的雙線性化,并構(gòu)造出超對稱柱KdV方程的單孤子解、雙孤子解、三孤子解以及n孤子解的表達(dá)形式。其次,由超對稱柱KdV方程的雙線性形式出發(fā),利用Wronskian行列式的性質(zhì)和Laplace定理構(gòu)造出具有Wronskian形式的孤子解,并驗證了 Wr onskian形式的孤子解與雙線性導(dǎo)數(shù)法求出的孤子解具有一致性。最后,以超對稱柱KdV方程雙線性形式為基礎(chǔ),利用超雙線性算子的定義和相關(guān)公式,得到了超對稱柱KdV方程的雙線性Backlund變換,然后利用已知解構(gòu)造出超對稱柱KdV方程的許多解。
[Abstract]:In this paper, the KdV equation of supersymmetric cylinder is studied. The three methods of solving nonlinear equation, bilinear derivative method and bilinear Backlund transform are generalized to the KdV equation of supersymmetric cylinder.Firstly, we use the direct method to supersymmetric the column KdV equation and obtain the KdV equation of the supersymmetric column.The bilinear linearization of the supersymmetric cylindrical KdV equation is derived by proper variable transformation, and the expressions of the single soliton solution, the double soliton solution, the three-soliton solution and the n-soliton solution of the supersymmetric cylindrical KdV equation are constructed.Secondly, based on the bilinear form of supersymmetric cylindrical KdV equation, the soliton solution with Wronskian form is constructed by using the property of Wronskian determinant and Laplace theorem.It is proved that the soliton solution in Wr onskian form is consistent with the soliton solution obtained by bilinear derivative method.Finally, based on the bilinear form of the supersymmetric cylinder KdV equation, the bilinear Backlund transformation of the supersymmetric cylinder KdV equation is obtained by using the definition of the superbilinear operator and the relevant formulas. Then many solutions of the supersymmetric cylinder KdV equation are constructed by using the known solutions.
【學(xué)位授予單位】：華東理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175.29

【共引文獻(xiàn)】

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2 彭釩;郝玉香;;加熱爐臺車的密封綜述[J];科技創(chuàng)新與應(yīng)用;2015年11期

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本文編號：1735815