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Abstract
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 potential 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 Hertztype systems.
Original language  English 

Article number  598 
Pages (fromto)  122 
Number of pages  22 
Journal  European Physical Journal Plus 
Volume  135 
Issue number  7 
DOIs  
Publication status  Published  Jul 2020 
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Dive into the research topics of 'On the generation and propagation of solitary waves in integrable and nonintegrable nonlinear lattices'. Together they form a unique fingerprint.Projects
 1 Finished

A new asymptotic toolbox for nonlinear discrete systems and particle chains
4/02/19 → 30/09/22
Project: Other