几个超对称方程的精确解
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��
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