Complex and coupled complex negative order AKNS equation

In this paper, we propose a complex negative order AKNS equation and a coupled complex negative order AKNS equation. They are integrable due to the existence of Lax pairs. Furthermore, we find their multi-soliton solutions in terms of Pfaffians by virtue of Hirota's bilinear method. One- and two-soliton solutions are investigated in detail exhibiting favorable evolution properties. Especially, the same as the coupled nonlinear Schrödinger equation, inelastic interactions and energy re-distribution happen between two solitons, that has potential applications and deserve further study.