A Nonstandard Supersymmetric KP Hierarchy
J. C. Brunelli, A. Das
TL;DR
This paper introduces a nonstandard supersymmetric KP hierarchy, linking it to known equations like super mKdV and KP, and constructs a new nonlocal super KP equation with conserved charges.
Contribution
It presents a novel nonstandard supersymmetric KP hierarchy and derives a new nonlocal super KP equation, expanding the understanding of supersymmetric integrable systems.
Findings
The supersymmetric nonlinear Schrödinger equation can be expressed as a constrained super KP flow.
The hierarchy reduces to super mKdV with proper identifications.
A new nonlocal super KP equation is constructed.
Abstract
We show that the supersymmetric nonlinear Schr\"odinger equation can be written as a constrained super KP flow in a nonstandard representation of the Lax equation. We construct the conserved charges and show that this system reduces to the super mKdV equation with appropriate identifications. We construct various flows generated by the general nonstandard super Lax equation and show that they contain both the KP and mKP flows in the bosonic limits. This nonstandard supersymmetric KP hierarchy allows us to construct a new super KP equation which is nonlocal.
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