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 Rapid fixation of deleterious alleles can be caused by Muller's ratchet

1997 ◽  
Vol 70 (1) ◽  
pp. 63-73 ◽  
Author(s):  
BRIAN CHARLESWORTH ◽  
DEBORAH CHARLESWORTH
Keyword(s):  
Analytical Approximation ◽  
Similar Process ◽  
Asexual Population ◽  
Single Chromosome ◽  
Muller's Ratchet ◽  
Analytical Approximations ◽  
Deleterious Alleles ◽  
Wide Range ◽  
Muller’S Ratchet ◽  
Parameter Values

Theoretical arguments are presented which suggest that each advance of Muller's ratchet in a haploid asexual population causes the fixation of a deleterious mutation at a single locus. A similar process operates in a diploid, fully asexual population under a wide range of parameter values, with respect to fixation within one of the two haploid genomes. Fixations of deleterious mutations in asexual species can thus be greatly accelerated in comparison with a freely recombining genome, if the ratchet is operating. In a diploid with segregation of a single chromosome, but no crossing over within the chromosome, the advance of the ratchet can be decoupled from fixation if mutations are sufficiently close to recessivity. A new analytical approximation for the rate of advance of the ratchet is proposed. Simulation results are presented that validate the assertions about fixation. The simulations show that none of the analytical approximations for the rate of advance of the ratchet are satisfactory when population size is large. The relevance of these results for evolutionary processes such as Y chromosome degeneration is discussed.

scholarly journals Ergodic and nonergodic many-body dynamics in strongly nonlinear lattices

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Dominik Hahn ◽  
Juan-Diego Urbina ◽  
Klaus Richter ◽  
Rémy Dubertrand ◽  
S. L. Sondhi
Keyword(s):  
Many Body ◽  
Strongly Nonlinear ◽  
Nonlinear Lattices ◽  
Body Dynamics

Small amplitude nonlinear electron acoustic solitary waves in weakly magnetized plasma

2013 ◽  
Vol 20 (1) ◽  
pp. 012113 ◽  
Author(s):  
Manjistha Dutta ◽  
Samiran Ghosh ◽  
Rajkumar Roychoudhury ◽  
Manoranjan Khan ◽  
Nikhil Chakrabarti
Keyword(s):  
Solitary Waves ◽  
Small Amplitude ◽  
Magnetized Plasma ◽  
Electron Acoustic

A regularized model for strongly nonlinear internal solitary waves

2009 ◽  
Vol 629 ◽  
pp. 73-85 ◽  
Author(s):  
WOOYOUNG CHOI ◽  
RICARDO BARROS ◽  
TAE-CHANG JO
Keyword(s):  
Stability Analysis ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Wave Solution ◽  
Wave Amplitude ◽  
Solitary Wave Solution ◽  
Shear Instability ◽  
Internal Solitary Waves ◽  
Strongly Nonlinear ◽  
Regularized Model

The strongly nonlinear long-wave model for large amplitude internal waves in a two-layer system is regularized to eliminate shear instability due to the wave-induced velocity jump across the interface. The model is written in terms of the horizontal velocities evaluated at the top and bottom boundaries instead of the depth-averaged velocities, and it is shown through local stability analysis that internal solitary waves are locally stable to perturbations of arbitrary wavelengths if the wave amplitudes are smaller than a critical value. For a wide range of depth and density ratios pertinent to oceanic conditions, the critical wave amplitude is close to the maximum wave amplitude and the regularized model is therefore expected to be applicable to the strongly nonlinear regime. The regularized model is solved numerically using a finite-difference method and its numerical solutions support the results of our linear stability analysis. It is also shown that the solitary wave solution of the regularized model, found numerically using a time-dependent numerical model, is close to the solitary wave solution of the original model, confirming that the two models are asymptotically equivalent.

scholarly journals On the Dynamics of Two-Dimensional Capillary-Gravity Solitary Waves with a Linear Shear Current

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Dali Guo ◽  
Bo Tao ◽  
Xiaohui Zeng
Keyword(s):  
Solitary Waves ◽  
Gravity Waves ◽  
Small Amplitude ◽  
Numerical Study ◽  
Two Dimensional ◽  
Shear Current ◽  
Linear Shear ◽  
The Stability ◽  
Depression Wave ◽  
Elevation Wave

The numerical study of the dynamics of two-dimensional capillary-gravity solitary waves on a linear shear current is presented in this paper. The numerical method is based on the time-dependent conformal mapping. The stability of different kinds of solitary waves is considered. Both depression wave and large amplitude elevation wave are found to be stable, while small amplitude elevation wave is unstable to the small perturbation, and it finally evolves to be a depression wave with tails, which is similar to the irrotational capillary-gravity waves.

scholarly journals Computational and Numerical Solutions for 2+1-Dimensional Integrable Schwarz–Korteweg–de Vries Equation with Miura Transform

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Raghda A. M. Attia ◽  
S. H. Alfalqi ◽  
J. F. Alzaidi ◽  
Mostafa M. A. Khater ◽  
Dianchen Lu
Keyword(s):  
Solitary Waves ◽  
Decomposition Method ◽  
Numerical Solutions ◽  
Vries Equation ◽  
Adomian Decomposition Method ◽  
Simplest Equation Method ◽  
Adomian Decomposition ◽  
Tanh Method ◽  
De Vries ◽  
Parameter Values

This paper investigates the analytical, semianalytical, and numerical solutions of the 2+1–dimensional integrable Schwarz–Korteweg–de Vries (SKdV) equation. The extended simplest equation method, the sech-tanh method, the Adomian decomposition method, and cubic spline scheme are employed to obtain distinct formulas of solitary waves that are employed to calculate the initial and boundary conditions. Consequently, the numerical solutions of this model can be investigated. Moreover, their stability properties are also analyzed. The solutions obtained by means of these techniques are compared to unravel relations between them and their characteristics illustrated under the suitable choice of the parameter values.

PROPAGATION OF SOLITARY WAVES ON LOSSY NONLINEAR TRANSMISSION LINES

2009 ◽  
Vol 23 (01) ◽  
pp. 1-18 ◽  
Author(s):  
E. KENGNE ◽  
R. VAILLANCOURT
Keyword(s):  
Solitary Waves ◽  
Transmission Lines ◽  
Small Amplitude ◽  
Reductive Perturbation Method ◽  
Ginzburg Landau ◽  
Nonlinear Transmission Lines ◽  
Nonlinear Transmission ◽  
Long Wavelength ◽  
Reductive Perturbation ◽  
Ginzburg Landau Equations

We present a lossy nonlinear transmission RLC line and show how the coupled Ginzburg–Landau equations can be derived in the small amplitude and long wavelength limit using a standard reductive perturbation method and complex expansion. Soliton-like solution of the simplified equation was searched and the instability of a class of phase-winding solutions was explored.

scholarly journals (2 + 1)-Dimensional Coupled Model for Envelope Rossby Solitary Waves and Its Solutions as well as Chirp Effect

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Xin Chen ◽  
Hongwei Yang ◽  
Min Guo ◽  
Baoshu Yin
Keyword(s):  
Solitary Waves ◽  
Rossby Waves ◽  
Modulation Instability ◽  
Multiple Scales ◽  
Coupled Model ◽  
Nls Equation ◽  
Coupled Models ◽  
Trial Function Method ◽  
Rossby Solitary Waves ◽  
Stable Feature

Using the method of multiple scales and perturbation method, a set of coupled models describing the envelope Rossby solitary waves in (2+1)-dimensional condition are obtained, also can be called coupled NLS (CNLS) equations. Following this, based on trial function method, the solutions of the NLS equation are deduced. Moreover, the modulation instability of coupled envelope Rossby waves is studied. We can find that the stable feature of coupled envelope Rossby waves is decided by the value of S. Finally, learning from the concept of chirp in the optical soliton communication field, we study the chirp effect caused by nonlinearity and dispersion in the propagation of Rossby waves.

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