Modified scattering for the nonlinear Pauli equation in the uniform magnetic field

Yilin Song; Ruixiao Zhang; Jiqiang Zheng

doi:10.3934/dcds.2026017

Article Contents

2026, Volume 50: 489-535. Doi: 10.3934/dcds.2026017

This volume Previous Article Quantitative convergence guarantees for the mean-field dispersion process Next Article Global existence and optimal time-decay rates of the compressible Navier-Stokes equations with density-dependent viscosities

Modified scattering for the nonlinear Pauli equation in the uniform magnetic field

1.
The Graduate School of China Academy of Engineering Physics, Beijing 100088, China
2.
Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China
3.
National Key Laboratory of Computational Physics, Beijing 100088, China

^*Corresponding author: Jiqiang Zheng
^*Corresponding author: Jiqiang Zheng

Received: May 9, 2025

Revised: December 9, 2025

Early access: December 22, 2025

Published online: December 22, 2025

J. Zheng was supported by NSF grant of China (No. 12271051).

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Abstract

In this paper, we investigate the long-time behavior of the nonlinear Pauli-type equation under the uniform magnetic confinement in dimension three. In scalar form, the Pauli equation can be expressed as a two-component coupled cubic nonlinear Schrödinger system with the external uniform magnetic potential. This type model appears in the investigation of rotating Bose-Einstein condensation. Building upon the pioneering works of Hani-Pausader-Tzvetkov-Visciglia [Forum Math. Pi, 3 (2015), 63pp] and Hani-Thomann [Commun. Pure Appl. Math. 69 (2016), 1727-1776], we first establish the modified scattering for this coupled system and construct the modified wave operators by using the normal form reduction and reducing the nonlinear equations to the resonant system. Moreover, we can show that the solution to the nonlinear Pauli equation converges to the nonlinear Schrödinger equation with averaged nonlinearity globally in time, which generalizes the work of Frank-Méhats-Sparber [Commun. Math. Sci. 15 (2017), 1933-1945].

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Mathematics Subject Classification: Primary: 35Q55; Secondary: 35L05.

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References

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