Work

Transverse dependence and asymptotic dimensional reduction of ground states for the logarithmic Schrödinger equation on a waveguide manifold

Year: 2025

Type: preprint

Abstract: In this paper, we develop a novel approach to studying the $y$-dependence of ground states for the logarithmic Schrödinger equation on $\mathbb{R}^d \times \mathbb{T}$. Unlike in \cite{STNT2014} (Analysis \& PDE, 2014) and \cite{HH1} (SIAM J. Math. Anal., 2024), the power-law scaling argument does not transfer directly to the logarithmic setting. Instead, amplitude scaling gives an exact identity showing that transverse dependence is independent of the prescribed mass. We also discuss uniqueness for the Cauchy problem and conditional orbital stability.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2505.23403

Authors: Wang, Jun, Hajaiej, Hichem, Yin, Zhaoyang

Institutions: Sun Yat-sen University, Shenzhen University, The Seventh Affiliated Hospital of Sun Yat-sen University

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Award: G6036389130

OpenAlex ID: W4416611604

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