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

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 n