时间周期边界条件下聚焦Kundu-Eckhaus方程的渐近孤子

Asymptotic solitons of the focusing Kundu-Eckhaus equation with time-periodic boundary condition

本文研究四分之一平面上的聚焦Kundu-Eckhaus方程,其初始数据在无穷远处消失,同时边界数据是时间周期的,它的形式为ae^(iδ)e^(2iωt).首先,推导出一个Riemann-Hilbert问题,它的解能够产生初边值问题的解.此外,研究结果表明,当ω<-3a^(2)/2-3β^(2)a^(4)时,初边值问题的解在不同的区域有不同的渐近行为.特别地,对于渐近孤子区域,初边值问题的解是渐近孤子序列的渐近解.

In this paper,we investigate the focusing Kundu-Eckhaus equation on the quarter plane.The initial data vanish at infinity while the boundary data are time-periodic,which are of the form ae^(iδ)e^(2iωt).Firstly,we derive a Riemann-Hilbert problem whose solution yields the solution to our IBV(initial boundary value) problem.Moreover,we find that for ω -3a^(2)/2-3β^(2)a^(4),the solution of the IBV problem has different asymptotic behaviors in different regions.In particular,for the asymptotic solitons region,the solution of the IBV problem is asymptotic to a series of asymptotic solitons.