An Integrable Evolution System and Its Analytical Solutions with the Help of Mixed Spectral AKNS Matrix Problem

In this work, a novel integrable evolution system in the sense of Lax’s scheme associated with mixed spectral Ablowitz-Kaup-Newell-Segur (AKNS) matrix problem is first derived. Then, time dependences scattering data corresponding to AKNS are given inverse analysis. Based on data, reconstruction potentials carried out, and finally analytical solutions four arbitrary functions derived formulated. This study shows that some other systems equations under resolvable framework method parameters can be constructed by embedding different time-varying coefficient known problem.