Long-time reduction for the biharmonic nonlinear Schrödinger equation

Younghun Hong; Junyeong Jang

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arXiv · 2609.30681

Long-time reduction for the biharmonic nonlinear Schrödinger equation

Younghun Hong·Junyeong Jang

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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 $H^s$--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.

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Younghun Hong, Junyeong Jang. 2026-09-25. Long-time reduction for the biharmonic nonlinear Schrödinger equation. https://arxiv.org/abs/2609.30681

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