N=1 SKdV新守恒量的无穷序列与超对称上同调
Infinite sequence of new conserved quantities for N=1 SKdV and the supersymmetric cohomology
摘要：
得到了N=1 Super KdV（SKdV）方程的一个新的非定域守恒量的无穷序列.序列的构建，通过加德纳变换，从一个新的守恒量的超级加德纳方程。超对称生成元定义了从所有守恒量的空间到自身的幂零运算。在$C_\downarrow^\infty$超场环上，局部守恒量是封闭的，但不是精确的。然而，在$C_{NL,1}^\infty$超场的环上，$C_\downarrow^\infty$环的扩展，它们变得精确并且等于适当权重的奇非局部守恒量子集的SUSY变换。其余的奇非定域守恒量生成封闭的几何对象，当环扩展到$C_{NL,2}^\infty$超场时，这些封闭的几何对象变得精确，并且等于我们得到的新的偶非定域守恒量的SUSY变换。这些方程完全符合已知守恒量的超对称上同调。
英文摘要：
An infinite sequence of new non-local conserved quantities for N=1 Super KdV (SKdV) equation is obtained. The sequence is constructed, via a Gardner trasformation, from a new conserved quantity of the Super Gardner equation. The SUSY generator defines a nilpotent operation from the space of all conserved quantities into itself. On the ring of $C_\downarrow^\infty$ superfields the local conserved quantities are closed but not exact. However on the ring of $C_{NL,1}^\infty$ superfields, an extension of the $C_\downarrow^\infty$ ring, they become exact and equal to the SUSY transformed of the subset of odd non-local conserved quantities of the appropriate weight. The remaining odd no-local ones generate closed geometrical objects which become exact when the ring is extended to the $C_{NL,2}^\infty$ superfields and equal to the SUSY transformed of the new even non-local conserved quantities we have obtained. These ones fit exactly in the SUSY cohomology of the already known conserved quantities.
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