2021/09/16 by Xin Wu, Wu, Xin, Shou‐Fu Tian +1
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Advanced Mathematical Physics Problems #Nonlinear Photonic Systems
paper · pdf · doi:10.48550/arxiv.2109.07637
In this work, we investigate the long-time asymptotic behavior of the Wadati-Konno-Ichikawa equation with initial data belonging to Schwartz space at infinity by using the nonlinear steepest descent method of Deift and Zhou for the oscillatory Riemann-Hilbert problem. Based on the initial value condition, the original Riemann-Hilbert problem is constructed to express the solution of the Wadati-Konno-Ichikawa equation. Through a series of deformations, the original RH problem is transformed into a model RH problem, from which the long-time asymptotic solution of the equation is obtained explicitly.