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The method of simplest equation is applied for analysis of a class of lattices described by differential-difference equations that admit traveling-wave solutions constructed on the basis of the solution of the Riccati equation. We denote such lattices as Riccati lattices. We search for Riccati lattices within two classes of lattices: generalized Lotka - Volterra lattices and generalized Holling lattices. We show that from the class of generalized Lotka - Volterra lattices only the Wadati lattice belongs to the class of Riccati lattices. Opposite to this many lattices from the Holling class are Riccati lattices. We construct exact traveling wave solutions on the basis of the solution of Riccati equation for three members of the class of generalized Holing lattices.
We describe the dynamic response of a two-dimensional hexagonal packing of uncompressed stainless steel spheres excited by localized impulsive loadings. After the initial impact strikes the system, a characteristic wave structure emerges and continuo
Based on the notion of Darboux-KP chain hierarchy and its invariant submanifolds we construct some class of constraints compatible with integrable lattices. Some simple examples are given.
This paper studies the differential lattice, defined to be a lattice $L$ equipped with a map $d:Lto L$ that satisfies a lattice analog of the Leibniz rule for a derivation. Isomorphic differential lattices are studied and classifications of different
We investigate the generation and propagation of solitary waves in the context of the Hertz chain and Toda lattice, with the aim to highlight the similarities, as well as differences between these systems. We begin by discussing the kinetic and poten
We consider the symmetries of coincidence site lattices of 3-dimensional cubic lattices. This includes the discussion of the symmetry groups and the Bravais classes of the CSLs. We derive various criteria and necessary conditions for symmetry operati