Discrete potential Ablowitz–Kaup–Newell–Segur equation. Issue 8 (3rd August 2019) - Zhao, Song-lin
Abstract : We establish a discrete model for the potential Ablowitz–Kaup–Newell–Segur equation via a generalized Cauchy matrix approach. Soliton solutions and Jordan block solutions of this equation are presented by solving the determining equation set. By applying appropriate continuum limits, we obtain two semi-discrete potential Ablowitz–Kaup–Newell–Segur equations. The reductions to real and complex discrete and semi-discrete potential modified Korteweg-de Vries equations are also discussed.