Long-time asymptotics for the focusing coupled Kundu-Eckhaus equation
Abstract
We prove global well-posedness in the Schwartz space and establish long-time asymptotics for the focusing coupled Kundu--Eckhaus (CKE) equation. For data with no discrete spectrum or real-axis spectral singularities, we analyze the associated matrix Riemann--Hilbert problem by the Deift--Zhou nonlinear steepest descent method. A quantitative local expansion of the full matrix factor near the stationary point identifies the unitary factor in the leading vector term. We combine an estimate for the full matrix coefficient at infinity with exact mass identities. This gives joint error estimates for the gauge-equivalent coupled nonlinear Schrödinger solution, the cumulative mass, and the gauge phase. These joint estimates yield an explicit asymptotic formula for CKE radiation with an O(t−1log t) remainder, uniformly for x/t in compact subsets of ℝ. We also compute the reflection coefficient and the unitary endpoint factor to visualize the asymptotic solution.
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BibTeX
@misc{qiu2026longtime,
title = {{Long-time asymptotics for the focusing coupled Kundu-Eckhaus equation}},
author = {Tianwei Qiu and Zhen Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16564},
eprint = {2610.16564},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16564},
}
RIS
TY - UNPB
TI - Long-time asymptotics for the focusing coupled Kundu-Eckhaus equation
AU - Tianwei Qiu
AU - Zhen Wang
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16564
UR - https://arxiv.org/abs/2610.16564
AB - We prove global well-posedness in the Schwartz space and establish long-time asymptotics for the focusing coupled Kundu--Eckhaus (CKE) equation. For data with no discrete spectrum or real-axis spectral singularities, we analyze the associated matrix Riemann--Hilbert problem by the Deift--Zhou nonlinear steepest descent method. A quantitative local expansion of the full matrix factor near the stationary point identifies the unitary factor in the leading vector term. We combine an estimate for the full matrix coefficient at infinity with exact mass identities. This gives joint error estimates for the gauge-equivalent coupled nonlinear Schrödinger solution, the cumulative mass, and the gauge phase. These joint estimates yield an explicit asymptotic formula for CKE radiation with an O(t^−1log t) remainder, uniformly for x/t in compact subsets of ℝ. We also compute the reflection coefficient and the unitary endpoint factor to visualize the asymptotic solution.
ER -