Cauchy matrix solutions of some local and nonlocal complex equations

We develop a Cauchy matrix reduction technique that enables us to obtain solutions for the reduced local and nonlocal complex equations from of original nonreduced systems. Specifically, by imposing reductions on some Ablowitz–Kaup–Newell–Segur-type equations, we study involving modified Korteweg–de Vries equation, sine-Gordon potential nonlinear Schrödinger equation. matrix-type soliton Jordan block aforesaid are presented. The dynamical behavior obtained is analyzed with graphical illustrations.