اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn traveling waves in lattices: The case of Riccati lattices
198
0
0.0
(
0
)
تأليف
Zlatinka I. Dimitrova
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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.
قيم البحث
اقرأ أيضاً
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
usly decays as it propagates through the lattice. Using an extension of the binary collision approximation (BCA) for one-dimensional chains, we predict its decay rate, which compares well with numerical simulations and experimental data. While the hexagonal lattice does not support constant speed traveling waves, we provide scaling relations that characterize the power law decay of the wave velocity. Lastly, we discuss the effects of weak disorder on the directional amplitude decay rates.
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
ial lattices are obtained for some basic lattices. Several families of derivations on a lattice are explicitly constructed, giving realizations of the lattice as lattices of derivations. Derivations on a finite distributive lattice are shown to have a natural structure of lattice. Moreover, derivations on a complete infinitely distributive lattice form a complete lattice. For a general lattice, it is conjectured that its poset of derivations is a lattice that uniquely determines the given lattice.
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
tial energy of a solitary wave in these systems, and show that under certain circumstances the kinetic and potential energy profiles in these systems (i.e., their spatial distribution) look reasonably close to each other. While this and other features, such as the connection between the amplitude and the total energy of the wave bear similarities between the two models, there are also notable differences, such as the width of the wave. We then study the dynamical behavior of these systems in response to an initial velocity impulse. For the Toda lattice, we do so by employing the inverse scattering transform, and we obtain analytically the ratio between the energy of the resulting solitary wave and the energy of the impulse, as a function of the impulse velocity; we then compare the dynamics of the Toda system to that of the Hertz system, for which the corresponding quantities are obtained through numerical simulations. In the latter system, we obtain a universality in the fraction of the energy stored in the resulting solitary traveling wave irrespectively of the size of the impulse. This fraction turns out to only depend on the nonlinear exponent. Finally, we investigate the relation between the velocity of the resulting solitary wave and the velocity of the impulse. In particular, we provide an alternative proof for the numerical scaling rule of Hertz type systems.
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
ons of CSLs. They are used to obtain a complete list of the symmetry groups and the Bravais classes of those CSLs that are generated by a rotation through the angle $pi$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
