Abstract
The fermionic covariant prolongation structure theory is investigated. We extend the fermionic covariant prolongation structure technique to the multidimensional super nonlinear evolution equation and present the fermionic covariant fundamental equations determining the prolongation structure. Furthermore, we investigate a (2+1)-dimensional super nonlinear Schrödinger equation and analyze its integrability by means of this prolongation structure technique. We derive its Lax representation and Bäcklund transformation. Moreover, we present a solution of this multidimensional super integrable equation.
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