Exploring supersymmetric negative order AKNS equation: Darboux transformation and multi-soliton solutions

Negative order flow hierarchies are of much consideration because of new novel findings not only from the point of integrability but also give insight underlying phenomena dynamically. In this paper, we develop and study the supersymmetric negative order AKNS equation. We explore the Darboux transformation of supersymmetric negative order AKNS not only for a matrix form but also on a component form. We derive the superfield multi-soliton solutions of the system through the iteration of Darboux matrix. As an explicit example, we present soliton solutions for the [Formula: see text] and [Formula: see text] case. The findings provide novel, impactful and intriguing perspectives, encouraging the readers to explore this system further.