TY - JOUR
AU - Fan, Engui
AB - The authors study the Cauchy problem for the focusing nonlinear Kundu-Eckhaus (KE for short) equation and construct the long time asymptotic expansion of its solution in fixed space-time cone with C(x1, x2, v1, v2) = {(x, t) ∈ ℝ2 : x = x0 + vt, x0 ∈ [x1, x2], v ∈ [v1, v2]}. By using the inverse scattering transform, Riemann-Hilbert approach and \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\overline{\partial}$$\end{document} 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 \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\cal{O}(t^{-{3\over 4}})$$\end{document}.
TI - Long Time Asymptotics Behavior of the Focusing Nonlinear Kundu-Eckhaus Equation
JF - Chinese Annals of Mathematics Series B
DO - 10.1007/s11401-023-0012-2
DA - 2023-03-01
UR - https://www.deepdyve.com/lp/springer-journals/long-time-asymptotics-behavior-of-the-focusing-nonlinear-kundu-eckhaus-2p01A1180Y
SP - 235
EP - 264
VL - 44
IS - 2
DP - DeepDyve
ER -