Long time asymptotic for the Wadati-Konno-Ichikawa equation with finite density initial data

2021/09/14 by Li, Zhi-Qiang, Tian, Shou-Fu, Yang, Jin-Jie
#Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2109.06384

Abstract

In this work, we investigate the Cauchy problem of the Wadati-Konno-Ichikawa (WKI) equation with finite density initial data. Employing the ∂-generalization of Deift-Zhou nonlinear steepest descent method, we derive the long time asymptotic behavior of the solution q(x,t) in space-time soliton region. Based on the resulting asymptotic behavior, the asymptotic approximation of the WKI equation is characterized with the soliton term confirmed by N(I)-soliton on discrete spectrum and the t^-(1)/(2) leading order term on continuous spectrum with residual error up to O(t^-(3)/(4)). Our results also confirm the soliton resolution conjecture for the WKI equation with finite density initial data.

Related

• Long-time asymptotics for the Wadati-Konno-Ichikawa equation with the Schwartz initial data
• Global solution of the Wadati-Konno-Ichikawa equation with small initial data
• Soliton resolution, asymptotic stability and Painlevé transcendents in the combined Wadati-Konno-Ichikawa and short-pulse equation
• Long-time asymptotic behavior for the complex short pulse equation
• Long-time asymptotic behavior of the nonlocal nonlinear Schrödinger equation with finite density type initial data