| Abstract: |
| This study focuses on the modulational dynamics of wave packets propagating in a one-dimensional (1D) hybrid Fermi-Pasta-Ulam-Tsingou / Klein-Gordon (FPUT-KG) type lattice chain, incorporating an arbitrary polynomial coupling potential anharmonicity combined with the presence of a nonlinear on-site (substrate) potential. Applying Newell`s multiple scales method, we have derived a Nonlinear Schrodinger type equation (NLSE) and thus obtained analytical expressions for the dispersion and nonlinearity coefficients, in terms of the carrier wavenumber k and the intrinsic lattice configuration parameters. We have explored the conditions for different regimes to occur, in order to determine the type of envelope soliton solutions to be sustained. The analysis is extended to different types of coupling anharmonicity and onsite potential nonlinearity, offering insight into the interplay between these factors and the system's dynamical behavior. We have focused in particular on extreme amplitude envelope modes (freak waves), e.g. of the Peregrine soliton type, and on their dependence on the various intrinsic system parameter values [1].
Our results are relevant in various contexts where periodic systems (e.g. crystals) may occur. As a novel field of application, this research applies to the modeling of dust-lattice waves in dusty plasma crystals. The substrate potential in this case is provided by electrostatic trapping in laboratory experiments, in combination with gravity, while the inter-site interaction potential is essentially of Debye-Hueckel type. This relation with be briefly discussed, and some preliminary results will be presented [2].
[1] Aysha Nihidha Pulakkal et al, in preparation (2026).
[2] I. Kourakis & P. K. Shukla, Int. J. Bifurcation & Chaos 16, 1711 (2006). |
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