scholarly journals On the generation and propagation of solitary waves in integrable and nonintegrable nonlinear lattices

2020 ◽  
Vol 135 (7) ◽  
Author(s):  
Guo Deng ◽  
Gino Biondini ◽  
Surajit Sen ◽  
Panayotis G. Kevrekidis
Keyword(s):  
Solitary Waves ◽  
Nonlinear Lattices

scholarly journals Travelling breathers and solitary waves in strongly nonlinear lattices

2018 ◽  
Vol 376 (2127) ◽  
pp. 20170138 ◽  
Author(s):  
Guillaume James
Keyword(s):  
Solitary Waves ◽  
Small Amplitude ◽  
Analytical Approximation ◽  
Discrete Elements ◽  
Nls Equation ◽  
Strongly Nonlinear ◽  
Analytical Approximations ◽  
Nearest Neighbours ◽  
Nonlinear Lattices ◽  
Parameter Values

We study the existence of travelling breathers and solitary waves in the discrete p -Schrödinger (DpS) equation. This model consists of a one-dimensional discrete nonlinear Schrödinger (NLS) equation with strongly nonlinear inter-site coupling (a discrete p -Laplacian). The DpS equation describes the slow modulation in time of small amplitude oscillations in different types of nonlinear lattices, where linear oscillators are coupled to nearest-neighbours by strong nonlinearities. Such systems include granular chains made of discrete elements interacting through a Hertzian potential ( p  = 5/2 for contacting spheres), with additional local potentials or resonators inducing local oscillations. We formally derive three amplitude PDEs from the DpS equation when the exponent of nonlinearity is close to (and above) unity, i.e. for p lying slightly above 2. Each model admits localized solutions approximating travelling breather solutions of the DpS equation. One model is the logarithmic NLS equation which admits Gaussian solutions, and the other is fully nonlinear degenerate NLS equations with compacton solutions. We compare these analytical approximations to travelling breather solutions computed numerically by an iterative method, and check the convergence of the approximations when . An extensive numerical exploration of travelling breather profiles for p  = 5/2 suggests that these solutions are generally superposed on small amplitude non-vanishing oscillatory tails, except for particular parameter values where they become close to strictly localized solitary waves. In a vibro-impact limit where the parameter p becomes large, we compute an analytical approximation of solitary wave solutions of the DpS equation. This article is part of the theme issue ‘Nonlinear energy transfer in dynamical and acoustical systems’.

scholarly journals Solitary Waves and Their Linear Stability in Nonlinear Lattices

2011 ◽  
Vol 128 (3) ◽  
pp. 275-298 ◽  
Author(s):  
G. Hwang ◽  
T. R. Akylas ◽  
J. Yang
Keyword(s):  
Linear Stability ◽  
Solitary Waves ◽  
Nonlinear Lattices

scholarly journals Discrete embedded solitary waves and breathers in one-dimensional nonlinear lattices

2021 ◽  
pp. 127880
Author(s):  
Faustino Palmero ◽  
Mario I. Molina ◽  
Jesús Cuevas-Maraver ◽  
Panayotis G. Kevrekidis
Keyword(s):  
Solitary Waves ◽  
One Dimensional ◽  
Nonlinear Lattices

Solitary waves in two-dimensional nonlinear lattices

2017 ◽  
Vol 228 (9) ◽  
pp. 3155-3171 ◽  
Author(s):  
Wei Wang ◽  
Liping Liu
Keyword(s):  
Solitary Waves ◽  
Two Dimensional ◽  
Nonlinear Lattices

Solitary waves on manifolds of integrate-and-fire neurons

1998 ◽  
Vol 77 (5) ◽  
pp. 1575-1583
Author(s):  
David Horn, Irit Opher
Keyword(s):  
Solitary Waves ◽  
Integrate And Fire
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