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摘要：可积系统在数学和物理中具有重要地位，所以研究其超对称化具有重要意义.而对于研究超对称可积理论的研究，求解其精确解是其中极为重要的一环.本文在介绍超对称理论的基础上给出了将孤子方程超对称化的具体步骤，并着重考究Hirota 双线性方法在超对称 KdV、1 SKdV方程中的应用求解. 众所周知 KdV 方程在N=2 可积空间中有两种扩张方式.他们都可以写成与第二类 KdV 结构的 N=2 的超对称形式相符合的带有普通泊松结构的哈密顿系统.通过分析共用哈密尔顿结构的方程单参数族守恒定律，有人发现通过非平凡守恒律的存在可以得出第三系统.并推测它是可积的. 28536
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关键词：精确解；Hirota双线性方法；超对称 KdV方程；1 SKdV方程
The exact solution of several supersymmetry equations
Abstract: Integrable theory plays an important role in mathematic and physics, so it is meaningful to study its supersymmetry. And for the study of supersymmetric integrable theory, solving the exact solution is a very important part. In this article we give a brief introduction of supersymmetry theory, based of which we give the specific steps on how to translate solution equations to the supersymmetry equations, and put the main part on the application of Hirota bilinear method to solve several the supersymmetry equations of KdV and 1 SKdV. There are two known integrable N = 2 space supersymmetric extensions of the KdV equation. Both can be written as Hamiltonian systems with a common Poisson structure which corresponds to the N = 2 supersymmetric form of the second KdV structure. By analyzing the conservation laws of the one parameter family of equations that share this Hamiltonian structure, one finds that a third system is singled out by the existence of nontrivial conservation laws. It is conjectured to be integrable. Key words: The exact solution; Hirota bilinear method; the supersymmetry equations of KdV; the equation of1 SKdV.
目录
摘要.1
引言.2
1超对称理论.3
2Hirota双线性方法.4
2.1双线性导数的定义及性质.4
2.2Hirota双线性法的具体步骤5
3双线性方法在超对称KdV方程中的应用8
3.1KdV方程的超对称化8
3.2求解超对称KdV方程.10
3.2.1超对称KdV方程的双线性化10
3.2.2超对称KdV方程的孤子解11
4双线性方法在
1SKdV
方程中的应用.14
4.1
1SKdV
方程14
4.2应用双线性方法求解
1SKdV
方程14
4.2.1
1SKdV
方程的双线性形式.14
4.2.2
1SKdV
方程的双线性解法.16
5一个新的N=2的超对称��