q-gap breathers and transition fronts beyond FPUT and in higher dimensions

Investigate the existence, dynamics, and approximation theory of q-gap breathers and transition fronts in higher-dimensional time-modulated nonlinear lattices and in systems beyond the Fermi–Pasta–Ulam–Tsingou model, including photonic, phononic, electrical, and other time-periodic media that exhibit wavenumber band gaps.

Background

The analysis and proofs in the paper focus on one-dimensional time-periodic FPUT lattices. Motivated by broad experimental and theoretical interest in time-varying systems across multiple domains (e.g., photonics, phononics, electrical circuits), the authors identify the extension of q-gap breathers and transition fronts to higher spatial dimensions and to other nonlinear time-periodic systems as an open direction.

Such generalizations would test the robustness of the normal-form and multiple-scale frameworks and potentially uncover new phenomena tied to multidimensional dispersion and band structure.