TY - JOUR TI - Inverse scattering transform for new mixed spectral Ablowitz-Kaup-Newell-Segur equations AU - Zhang Sheng AU - You Caihong JN - Thermal Science PY - 2020 VL - 24 IS - 4 SP - 2437 EP - 2444 PT - Article AB - The inverse scattering transform plays a very important role in promoting the development of analytical methods to solve non-linear PDE exactly. In this paper, new and more general mixed spectral Ablowitz-Kaup-Newell-Segur equations are derived and solved by embedding a novel time-varying spectral parameter in-to an associated linear problem and the inverse scattering transform. As a result, new exact solutions and n-soliton solutions are obtained. To gain more insights into the embedded spectral parameter and the obtained solutions, some dynamical evolutions, and spatial structures are simulated. It is shown that the derived Ablowitz-Kaup-Newell-Segur equations are Lax integrable and the obtained soliton solutions possess time-varying amplitudes.