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

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Abstract

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 \(\overline{\partial}\) 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 \(\cal{O}(t^{-{3\over 4}})\).

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Ruihong Ma & Engui Fan

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  1. Ruihong Ma
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  2. Engui Fan
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Correspondence to Ruihong Ma or Engui Fan.

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Ma, R., Fan, E. Long Time Asymptotics Behavior of the Focusing Nonlinear Kundu-Eckhaus Equation. Chin. Ann. Math. Ser. B 44, 235–264 (2023). https://doi.org/10.1007/s11401-023-0012-2

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  • DOI: https://doi.org/10.1007/s11401-023-0012-2

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