Long Time Asymptotics Behavior of the Focusing Nonlinear Kundu-Eckhaus Equation  

作　　者：Ruihong MA Engui FAN 

机构地区：[1]School of Mathematical Sciences,Fudan University,Shanghai 200433,China

出　　处：《Chinese Annals of Mathematics,Series B》2023年第2期235-264,共30页数学年刊（B辑英文版）

摘　　要：The authors study the Cauchy problem for the focusing nonlinear KunduEckhaus(KE for short)equation and construct the long time asymptotic expansion of its solution in fixed space-time cone with C(x_(1),x_(2),v_(1),v_(2))={(x,t)∈R^(2):x=x_(0)+vt,x_(0)∈[x_(1),x_(2)],v∈[v_(1),v_(2)]}.By using the inverse scattering transform,Riemann-Hilbert approach and δ steepest descent method,they obtain the lone time asymptotic behavior of the solution,at the same time,they obtain the solitons in the cone compare with the all N-soliton the residual error up to order O(t-^(3/4)).

关 键 词：Focusing Kundu-Eckhaus equation Riemann-Hilbert problem δsteepest descent method 

分 类 号：O175[理学—数学]