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- W4200536105 abstract "The problem of showing the existence of localised modes in nonlinear lattices has attracted considerable efforts from the physical but also from the mathematical viewpoint where a rich variety of methods has been employed. In this paper we prove that a fixed point theory approach based on the celebrated Schauder's Fixed Point Theorem may provide a general method to establish concisely not only the existence of localised structures but also a required rate of spatial localisation. As a case study we consider lattices of coupled particles with nonlinear nearest neighbour interaction and prove the existence of exponentially spatially localised breathers exhibiting either even-parity or odd-parity symmetry under necessary non-resonant conditions accompanied with the proof of energy bounds of the solutions." @default.
- W4200536105 created "2021-12-31" @default.
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- W4200536105 date "2021-12-01" @default.
- W4200536105 modified "2023-09-27" @default.
- W4200536105 title "Existence of exponentially spatially localized breather solutions for lattices of nonlinearly coupled particles: Schauder’s fixed point theorem approach" @default.
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- W4200536105 doi "https://doi.org/10.1063/5.0058381" @default.
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