Long time asymptotics behavior of the focusing nonlinear Kundu-Eckhaus equation

2019/12/01 by Ma, Ruihong, Fan, Engui
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences

paper · doi:10.48550/arxiv.1912.01425

Abstract

We study the Cauchy problem for the focusing nonlinear Kundu-Eckhaus equation and construct long time asymptotic expansion of its solution in fixed space-time cone with C(x₁,x₂,v₁,v₂)=\(x,t)∈\Re²:x=x₀+vt x₀∈[x₁,x₂],v∈[v₁,v₂] \. By using the inverse scattering transform, Riemann-Hilbert approach and ∂ steepest descent method we obtain the lone time asymptotic behavior of the solution, at the same time we obtain the solitons in the cone compare with the all N-soliton the residual error up to order O(t^-3/4).

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