Abstract
The Fermi-Pasta-Ulam problem together with the explanation by Zabusky and Kruskal can be rightly considered as the origin of lattice soli-tons. This problem is reviewed in some detail along with a nice integrable nonlinear lattice, the Toda lattice. The recurrence phenomenon in case of KdV system and FPU discrete limit is also discussed. Three diatomic nonlinear lattice models as well as their solutions are considered. These are the simplest cubic nonlinear model in continuum limit, diatomic Toda system and continuum model with nonlinear onsite potential at one of the mass points and harmonic potential at the other, connected by harmonic springs.
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References
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Dash, P.C. (1988). Lattice Solitons and Nonlinear Diatomic Models. In: Lakshmanan, M. (eds) Solitons. Springer Series in Nonlinear Dynamics . Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73193-8_13
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DOI: https://doi.org/10.1007/978-3-642-73193-8_13
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