PreprintarXiv licencearXiv
Long-time reduction for the biharmonic nonlinear Schrödinger equation
Abstract
In this article, we study the reduction of the one-dimensional biharmonic nonlinear Schrödinger equation to the cubic nonlinear Schrödinger equation in the vanishing higher-order dispersion limit. In the intermediate regularity regime 0<s<2, where the energy conservation law does not control the Hs--norm, we prove the long-time L2--convergence of Hs--solutions with an exponential-in-time approximation bound. The argument relies mainly on persistence of regularity. This result provides a simple example of its use in limit problems without relying on higher-order conservation laws.
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BibTeX
@misc{hong2026longtime,
title = {{Long-time reduction for the biharmonic nonlinear Schrödinger equation}},
author = {Younghun Hong and Junyeong Jang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30681},
eprint = {2609.30681},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30681},
}
RIS
TY - UNPB
TI - Long-time reduction for the biharmonic nonlinear Schrödinger equation
AU - Younghun Hong
AU - Junyeong Jang
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.30681
UR - https://arxiv.org/abs/2609.30681
AB - In this article, we study the reduction of the one-dimensional biharmonic nonlinear Schrödinger equation to the cubic nonlinear Schrödinger equation in the vanishing higher-order dispersion limit. In the intermediate regularity regime 0<s<2, where the energy conservation law does not control the H^s--norm, we prove the long-time L^2--convergence of H^s--solutions with an exponential-in-time approximation bound. The argument relies mainly on persistence of regularity. This result provides a simple example of its use in limit problems without relying on higher-order conservation laws.
ER -