2025/11/07 by Shi Cheng, Cheng Shi, Ross Parker +6 · 1 voice · 1 citation
Mathematics · Physics and Astronomy · #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #cond-mat.mtrl-sci #math-ph #math.SP #nlin.PS
paper · pdf · doi:10.48550/arxiv.2511.05671
arxiv published 2025/11/07 · arxiv updated 2025/11/25
We establish a sharp criterion for the stability of a class of compactly supported, homogeneous density``minimal compact solitons'' or MCS states, of the time-dependent discrete nonlinear Schrödinger equation on a multi-lattice, \mathbb L (\mathbb L-DNLS). MCS states arise for multi-lattices where a nearest neighbor Laplace-type operator on \mathbb L has a flat band. Our stability criterion is in terms of the explicit form of the nonlinearity and the projection of distinguished vectors onto the flat band eigenspace. We apply our general results to MCS states of DNLS for the diamond, Kagomé and checkerboard lattices. In lattices where MCS states are unstable, we demonstrate how to engineer the nonlinearity to stabilize small amplitude MCS states. Finally, via systematic numerical computations, we put our analytical results in the context of global bifurcation diagrams.