Nonlocal conservation laws in N=1,2 Supersymetric KdV equation
P. Dargis, P. Mathieu
TL;DR
This paper explores nonlocal conservation laws in N=1,2 supersymmetric KdV equations, revealing their connection to the Lax operator and demonstrating their existence in N=2 cases, thus linking supersymmetry and conservation laws.
Contribution
It establishes a simple relation between nonlocal conservation laws and powers of the Lax operator in N=1 supersymmetric KdV, and confirms their existence in N=2 cases.
Findings
Nonlocal conservation laws relate to powers of the Lax operator in N=1 supersymmetric KdV.
Nonlocal conservation laws exist for N=2 supersymmetric KdV equations.
A direct link between supersymmetry invariance and conservation laws is demonstrated.
Abstract
The \nl \cls for the N=1 supersymmetric KdV equation are shown to be related in a simple way to powers of the fourth root of its Lax operator. This provides a direct link between the supersymmetry invariance and the existence of \nl conservation laws. It is also shown that nonlocal conservation laws exist for the two integrable N=2 supersymmetric KdV equations whose recursion operator is known.
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