2022/05/17 by Hai-Jing Xu, Xu, Hai-Jing, Song-lin Zhao +1 · 1 citation
Mathematics · Physics and Astronomy · #35Q51 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:35Q51 #nlin.SI
paper · pdf · doi:10.48550/arxiv.2205.08214
28 pages,62 figures,to appear in Theor. Math. Phys
arxiv created 2022/05/17 · arxiv updated 2022/05/18
In this paper, we develop a Cauchy matrix reduction technique that enables us to obtain solutions for the reduced local and nonlocal complex equations from the Cauchy matrix solutions of the original before-reduction systems. Specifically, by imposing local and nonlocal complex reductions on some Ablowitz-Kaup-Newell-Segur-type equations, we study some local and nonlocal complex equations, involving the local and nonlocal complex modified Korteweg-de Vries equation, the local and nonlocal complex sine-Gordon equation, the local and nonlocal potential nonlinear Schrödinger equation and the local and nonlocal potential complex modified Korteweg-de Vries equation. Cauchy matrix-type soliton solutions and Jordan block solutions for the aforesaid local and nonlocal complex equations are presented. The dynamical behaviors of some obtained solutions are analyzed with graphical illustrations.