This analysis reveals exponential localization of solitary waves in 2D lattices, suggesting new insights into nonlinear particle interactions.
The article deals with the Fermi-Pasta-Ulam-type systems that describe infinite systems of nonlinearly coupled identical particles on two-dimensional lattices. It is assumed that every particle interacts nonlinearly with its four nearest neighbors. The main result concerns the exponential localization of solitary traveling-waves solutions in such systems. Using the Paley-Wiener theorem, the exponential estimate for the profiles of such solutions has been obtained.
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Бак et al. (2025) studied this question.
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