Abstract: In this paper, we study the general structure of evolution equations of the AKNS eigenvalue problem q(x,t), r(x,t) with the spectrum varying as and A₁,B₁,C₁are all positive or negative power polynomials of where q, r are not limited with any additional conditions at infinity.

Key words: AKNS eigenvalue problem, spectrum deformation, null curvature equation, general structure of evolution equation