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| Long Time Asymptotics Behavior of the Focusing Nonlinear Kundu-Eckhaus Equation |
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Citation： |
Ruihong MA,Engui FAN.Long Time Asymptotics Behavior of the Focusing Nonlinear Kundu-Eckhaus Equation[J].Chinese Annals of Mathematics B,2023,44(2):235~264 |
| Page view： 641
Net amount： 567 |
Authors： |
Ruihong MA; Engui FAN |
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| Abstract： |
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(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 ? 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 ). |
Keywords： |
Focusing Kundu-Eckhaus equation, Riemann-Hilbert problem,∂ steepest descent method |
Classification： |
O175.24 |
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