Soliton resolution and asymptotic stability of N-solutions for the defocusing Kundu–Eckhaus equation with nonzero boundary conditions  

作　　者：Engui Fan Yanxi Zhang 

机构地区：[1]School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Science,Fudan University,Shanghai,200433,China [2]Tianjin Xinhua High School,No.99 machang Road,Tianjin,300204,China

出　　处：《Communications in Theoretical Physics》2024年第1期1-6,共6页理论物理通讯（英文版）

基　　金：supported by the National Science Foundation of China(Grant No.12271104,51879045)。

摘　　要：In this paper,we address interesting soliton resolution,asymptotic stability of N-soliton solutions and the Painleve asymptotics for the Kundu-Eckhaus(KE)equation with nonzero boundary conditions iq_(t)+q_(xx)-2(l|q|^(2)-1)q+4β^(2)(lql^(4)-1)q+4iβ(lql^(2))_(x)q=0,q(x,0)=q_(0)(x)-±1,x→±∞.The key to proving these results is to establish the formulation of a Riemann-Hilbert(RH)problem associated with the above Cauchy problem and find its connection with the RH problem of the defocusing NLS equation.With the■-steepest descent method and the results of the defocusing NLS equation,we find complete leading order approximation formulas for the defocusing KE equation on the whole(x,t)half-plane including soliton resolution and asymptotic stability of N-soliton solutions in a solitonic region,Zakharov-Shabat asymptotics in a solitonless region and the Painlevéasymptotics in two transition regions.

关 键 词：defocusing Kundu-Eckhaus equation Riemann-Hilbert problems steepest descent method soliton resolution asymptotic stability Painleve transcendents 

分 类 号：O175[理学—数学]