Small-amplitude envelope solitons in nonlinear lattices

1996 ◽  
Vol 53 (3) ◽  
pp. 2843-2858 ◽  
Author(s):  
V. V. Konotop
Keyword(s):  
Small Amplitude ◽  
Amplitude Envelope ◽  
Envelope Solitons ◽  
Nonlinear Lattices

Capillary–gravity waves of solitary type and envelope solitons on deep water

1993 ◽  
Vol 252 ◽  
pp. 703-711 ◽  
Author(s):  
Michael S. Longuet-Higgins
Keyword(s):  
Surface Tension ◽  
Dispersion Relation ◽  
Gravity Waves ◽  
Deep Water ◽  
Small Amplitude ◽  
Finite Amplitude ◽  
Surface Slope ◽  
Carrier Wave ◽  
Envelope Solitons ◽  
Special Case

The existence of steady solitary waves on deep water was suggested on physical grounds by Longuet-Higgins (1988) and later confirmed by numerical computation (Longuet-Higgins 1989; Vanden-Broeck & Dias 1992). Their numerical methods are accurate only for waves of finite amplitude. In this paper we show that solitary capillary-gravity waves of small amplitude are in fact a special case of envelope solitons, namely those having a carrier wave of length 2π(T/ρg)1½2 (g = gravity, T = surface tension, ρ = density). The dispersion relation $c^2 = 2(1-\frac{11}{32}\alpha^2_{\max)$ between the speed c and the maximum surface slope αmax is derived from the nonlinear Schrödinger equation for deep-water solitons (Djordjevik & Redekopp 1977) and is found to provide a good asymptote for the numerical calculations.

Stability of two-dimensional finite-amplitude envelope solitons

1987 ◽  
Vol 35 (10) ◽  
pp. 4273-4279 ◽  
Author(s):  
R. Blaha ◽  
E. W. Laedke ◽  
K. H. Spatschek
Keyword(s):  
Finite Amplitude ◽  
Two Dimensional ◽  
Amplitude Envelope ◽  
Envelope Solitons

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’.

NONLINEAR TRANSPORT IN HYDROGEN-BONDED CHAINS: SOLITONS UNDER EXTERNAL FIELDS AND DAMPING

1994 ◽  
Vol 08 (08) ◽  
pp. 1033-1064 ◽  
Author(s):  
YU.S. KIVSHAR ◽  
A.V. SAVIN ◽  
M.J. VELGAKIS ◽  
A.V. ZOLOTARYUK
Keyword(s):  
Electric Field ◽  
External Electric Field ◽  
Small Amplitude ◽  
Nonlinear Transport ◽  
Dimensional Model ◽  
One Dimensional ◽  
Envelope Solitons ◽  
Oscillating Solutions ◽  
Two Parameter ◽  
Hydrogen Bonded

The longitudinal dynamics of protons in hydrogen-bonded chains is studied in the framework of a simple one-component one-dimensional model with a two-parameter doubly periodic symmetric on-site potential proposed by Zolotaryuk and Pnevmatikos (1990) under an external electric field and damping. The behavior of the ionic and bonding defects has been proved analytically and numerically to exhibit particle-like properties. Mobilities of the dc and ac driven defects have also been calculated with different methods. Small-amplitude oscillating solutions of breather and envelope solitons have been studied analytically and numerically.

Finite amplitude envelope solitons in a pair-ion plasma

2007 ◽  
Vol 14 (3) ◽  
pp. 032107 ◽  
Author(s):  
W. M. Moslem ◽  
I. Kourakis ◽  
P. K. Shukla
Keyword(s):  
Finite Amplitude ◽  
Amplitude Envelope ◽  
Envelope Solitons ◽  
Ion Plasma

Finite amplitude envelope solitons

1977 ◽  
Vol 20 (8) ◽  
pp. 1286 ◽  
Author(s):  
H. Schamel ◽  
M. Y. Yu ◽  
P. K. Shukla
Keyword(s):  
Finite Amplitude ◽  
Amplitude Envelope ◽  
Envelope Solitons
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