Multi-peak breather stability in a dissipative discrete Nonlinear Schrödinger (NLS) equation

2014 ◽  
Vol 23 (04) ◽  
pp. 1450044 ◽  
Author(s):  
Panayotis Panayotaros ◽  
Felipe Rivero
Keyword(s):  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Dissipation Parameter ◽  
Stabilizing Effect ◽  
Localized Forcing ◽  
The Stability

We study the stability of breather solutions of a dissipative cubic discrete NLS with localized forcing. The breathers are similar to the ones found for the Hamiltonian limit of the system. In the case of linearly stable multi-peak breathers the combination of dissipation and localized forcing also leads to stability, and the apparent damping of internal modes that make the energy around multi-peak breathers nondefinite. This stabilizing effect is however accompanied by overdamping for relatively small values of the dissipation parameter, and the appearance of near-zero stable eigenvalues.

Analytical simulations of the Fokas system; extension (2 + 1)-dimensional nonlinear Schrödinger equation

2021 ◽  
Author(s):  
Mostafa M. A. Khater
Keyword(s):  
Optical Fibers ◽  
Pulse Propagation ◽  
Dynamical Behavior ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Contour Plots ◽  
System Extension ◽  
Inverse Spectral Method ◽  
Nonlinear Pulse Propagation ◽  
The Stability

This paper studies novel analytical solutions of the extended [Formula: see text]-dimensional nonlinear Schrödinger (NLS) equation which is also known with [Formula: see text]-dimensional complex Fokas ([Formula: see text]D–CF) system. Fokas derived this system in 1994 by using the inverse spectral method. This model is considered as an icon model for nonlinear pulse propagation in monomode optical fibers. Many novel computational solutions are constructed through two recent analytical schemes (Ansatz and Projective Riccati expansion (PRE) methods). These solutions are represented through sketches in 2D, 3D, and contour plots to demonstrate the dynamical behavior of pulse propagation in breather, rogue, periodic, lump, and solitary characteristics. The stability property of the obtained solutions is examined based on the Hamiltonian system’s properties. The obtained solutions are checked by putting them back into the original equation through Mathematica 12 software.

scholarly journals Stability of multi-solitons in the cubic NLS equation

2014 ◽  
Vol 11 (02) ◽  
pp. 329-353 ◽  
Author(s):  
Andres Contreras ◽  
Dmitry Pelinovsky
Keyword(s):  
Initial Data ◽  
Inverse Scattering ◽  
Orbital Stability ◽  
Inverse Scattering Transform ◽  
Nls Equation ◽  
Transform Methods ◽  
Nonlinear Schrödinger ◽  
Scattering Transform ◽  
The Stability

We address the stability of multi-solitons for the cubic nonlinear Schrödinger (NLS) equation on the line. By using the dressing transformation and the inverse scattering transform methods, we establish the orbital stability of multi-solitons in the L2(ℝ) space when the initial data is in a weighted L2(ℝ) space.

scholarly journals Numerical investigation of stability of breather-type solutions of the nonlinear Schrödinger equation

2013 ◽  
Vol 1 (5) ◽  
pp. 5087-5115
Author(s):  
A. Calini ◽  
C. M. Schober
Keyword(s):  
Numerical Investigation ◽  
Rogue Waves ◽  
Maximal Dimension ◽  
Noisy Environments ◽  
Nls Equation ◽  
Stability Behavior ◽  
Nonlinear Schrödinger ◽  
Large Ensembles ◽  
The Stability ◽  
The One

Abstract. In this article we present the results of a broad numerical investigation on the stability of breather-type solutions of the nonlinear Schrödinger (NLS) equation, specifically the one- and two-mode breathers for an unstable plane wave, which are frequently used to model rogue waves. The numerical experiments involve large ensembles of perturbed initial data for six typical random perturbations. Ensemble estimates of the "closeness", A(t), of the perturbed solution to an element of the respective unperturbed family indicate that the only neutrally stable breathers are the ones of maximal dimension, that is: given an unstable background with N unstable modes, the only neutrally stable breathers are the N-dimensional ones (obtained as a superimposition of N simple breathers via iterated Backlund transformations). Conversely, breathers which are not fully saturated are sensitive to noisy environments and are unstable. Interestingly, A(t) is smallest for the coalesced two-mode breather indicating the coalesced case may be the most robust two-mode breather in a laboratory setting. The numerical simulations confirm and provide a realistic realization of the stability behavior established analytically by the authors.

scholarly journals Stabilizing effect of methylcellulose on the dispersion of multi-walled carbon nanotubes in cementitious composites

2020 ◽  
Vol 9 (1) ◽  
pp. 93-104
Author(s):  
Mingrui Du ◽  
Yuan Gao ◽  
Guansheng Han ◽  
Luan Li ◽  
Hongwen Jing
Keyword(s):  
Carbon Nanotubes ◽  
Pore Solution ◽  
Cementitious Materials ◽  
High Ionic Strength ◽  
Cementitious Composites ◽  
Uniform Distributions ◽  
Stabilizing Effect ◽  
Multi Walled Carbon Nanotubes ◽  
The Stability ◽  
Walled Carbon Nanotubes

AbstractMulti-walled carbon nanotubes (MWCNTs) have been added in the plain cementitious materials to manufacture composites with the higher mechanical properties and smart behavior. The uniform distributions of MWCNTs is critical to obtain the desired enhancing effect, which, however, is challenged by the high ionic strength of the cement pore solution. Here, the effects of methylcellulose (MC) on stabilizing the dispersion of MWCNTs in the simulated cement pore solution and the viscosity of MWCNT suspensions werestudied. Further observations on the distributions of MWCNTs in the ternary cementitious composites were conducted. The results showed that MC forms a membranous envelope surrounding MWCNTs, which inhibits the adsorption of cations and maintains the steric repulsion between MWCNTs; thus, the stability of MWCNT dispersion in cement-based composites is improved. MC can also work as a viscosity adjuster that retards the Brownian mobility of MWCNTs, reducing their re-agglomerate within a period. MC with an addition ratio of 0.018 wt.% is suggested to achieve the optimum dispersion stabilizing effect. The findings here provide a way for stabilizing the other dispersed nano-additives in the cementitious composites.

scholarly journals Evolution of a narrow-band spectrum of random surface gravity waves

2003 ◽  
Vol 478 ◽  
pp. 1-10 ◽  
Author(s):  
KRISTIAN B. DYSTHE ◽  
KARSTEN TRULSEN ◽  
HARALD E. KROGSTAD ◽  
HERVÉ SOCQUET-JUGLARD
Keyword(s):  
Three Dimensional ◽  
Low Frequency ◽  
Three Dimensions ◽  
Band Spectrum ◽  
Nls Equation ◽  
Random Surface ◽  
Narrow Bandwidth ◽  
Quasi Stationary State ◽  
The Stability ◽  
Three Dimensional Simulations

Numerical simulations of the evolution of gravity wave spectra of fairly narrow bandwidth have been performed both for two and three dimensions. Simulations using the nonlinear Schrödinger (NLS) equation approximately verify the stability criteria of Alber (1978) in the two-dimensional but not in the three-dimensional case. Using a modified NLS equation (Trulsen et al. 2000) the spectra ‘relax’ towards a quasi-stationary state on a timescale (ε2ω0)−1. In this state the low-frequency face is steepened and the spectral peak is downshifted. The three-dimensional simulations show a power-law behaviour ω−4 on the high-frequency side of the (angularly integrated) spectrum.

New Rational Homoclinic Solution and Rogue Wave Solution for the Coupled Nonlinear Schrödinger Equation

2014 ◽  
Vol 69 (8-9) ◽  
pp. 441-445 ◽  
Author(s):  
Long-Xing Li ◽  
Jun Liu ◽  
Zheng-De Dai ◽  
Ren-Lang Liu
Keyword(s):  
Schrödinger Equation ◽  
Wave Solution ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Homoclinic Solution ◽  
Nonlinear Schrodinger Equation ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Coupled Nonlinear Schrödinger Equation ◽  
Rogue Wave Solution

In this work, the rational homoclinic solution (rogue wave solution) can be obtained via the classical homoclinic solution for the nonlinear Schrödinger (NLS) equation and the coupled nonlinear Schrödinger (CNLS) equation, respectively. This is a new way for generating rogue wave comparing with direct constructing method and Darboux dressing technique

Optical solitons and stability analysis for the generalized fourth-order nonlinear Schrödinger equation

2019 ◽  
Vol 33 (27) ◽  
pp. 1950333
Author(s):  
Xiao-Song Tang ◽  
Biao Li
Keyword(s):  
Nonlinear Dynamics ◽  
Fourth Order ◽  
Continuous Wave ◽  
Modulational Instability ◽  
Optical Solitons ◽  
Singular Solutions ◽  
Nls Equation ◽  
Ansatz Method ◽  
Nonlinear Schrödinger ◽  
Wave Solutions

We consider a generalized fourth-order nonlinear Schrödinger (NLS) equation. Based on the ansatz method, its bright, dark single-soliton is constructed under some constraint conditions. Furthermore, combining the Riccati equation extension approach, we also derive some exact singular solutions. With several parameters to play with, we display the dynamic behaviors of bright, dark single-soliton. Finally, the condition for the modulational instability (MI) of continuous wave solutions for the equation is generated. It is hoped that our results can help enrich the nonlinear dynamics of the NLS equations.

scholarly journals Effect of Potato Pulp Pectic Polysaccharide on the Stability of Acidified Milk Drinks

Molecules ◽  
2020 ◽  
Vol 25 (23) ◽  
pp. 5632
Author(s):  
Weixuan Sun ◽  
Wenhan Yang ◽  
Yuxue Zheng ◽  
Huiling Zhang ◽  
Haitian Fang ◽  
...  
Keyword(s):  
Particle Size ◽  
Zeta Potential ◽  
Neutral Sugar ◽  
Lower Serum ◽  
Pectic Polysaccharide ◽  
Potato Pulp ◽  
Lower Viscosity ◽  
Stabilizing Effect ◽  
New Ideas ◽  
The Stability

In order to broaden the application of potato pulp pectic polysaccharide (PPP) in stabilizing acidified milk drinks (AMDs) and investigate the stabilizing effect and physical properties of AMDs prepared with PPP, a comparative study was made among PPP, commercial high methoxyl pectin (HMP) and low methoxyl pectin (LMP). The zeta potential, rheology, particle size and serum separation of AMDs were evaluated after preparing with PPP, HMP and LMP, respectively. Results indicated that PPP led to lower serum separation than LMP (14.65% for AMDs prepared with 0.5% PPP compared to 25.05% for AMDs prepared with 0.5% LMP), but still higher than HMP (9.09% for AMDs prepared with 0.5% HMP). However, narrower particle size distribution and lower viscosity of AMDs was achieved by PPP than by LMP and HMP. PPP can electrostatically adsorb on the surface of casein and its abundant neutral sugar side chains would provide steric hindrance to prevent casein flocculation in AMDs. Our results might provide some new ideas for the application of PPP in improving the stability of AMDs.

The almost complex structure on 𝕊6 and related Schrödinger flows

2018 ◽  
Vol 29 (14) ◽  
pp. 1850099 ◽  
Author(s):  
Qing Ding ◽  
Shiping Zhong
Keyword(s):  
Complex Structure ◽  
Type System ◽  
Text Structure ◽  
Almost Complex Structure ◽  
Nls Equation ◽  
Geometric Properties ◽  
Nonlinear Schrödinger ◽  
Almost Complex ◽  
Complex Functions

In this paper, by using the [Formula: see text]-structure on Im[Formula: see text] from the octonions [Formula: see text], the [Formula: see text]-binormal motion of curves [Formula: see text] in [Formula: see text] associated to the almost complex structure on [Formula: see text] is studied. The motion is proved to be equivalent to Schrödinger flows from [Formula: see text] to [Formula: see text], and also to a nonlinear Schrödinger-type system (NLSS) in three unknown complex functions that generalizes the famous correspondence between the binormal motion of curves in [Formula: see text] and the focusing nonlinear Schrödinger (NLS) equation. Some related geometric properties of the surface [Formula: see text] in Im[Formula: see text] swept by [Formula: see text] are determined.

Solutions of solitary-wave for the variable-coefficient nonlinear Schrödinger equation with two power-law nonlinear terms

2018 ◽  
Vol 32 (28) ◽  
pp. 1850310 ◽  
Author(s):  
Le Xin ◽  
Ying Kong ◽  
Lijia Han
Keyword(s):  
Solitary Wave ◽  
Power Law ◽  
Optical Lattice ◽  
Variable Coefficient ◽  
Transformation Method ◽  
Potential Space ◽  
Nls Equation ◽  
Quadratic Potential ◽  
Nonlinear Schrödinger ◽  
Constant Coefficients

In this paper, we consider the variable-coefficient power-law nonlinear Schrödinger equations (NLSEs) with external potential as well as the gain or loss function. First, we generalize the similarity transformation method, which converts the variable coefficient NLSE with two power-law nonlinear terms to the autonomous dual-power NLS equation with constant coefficients. Then, we obtain the exact solutions of the variable-coefficient NLSE. Moreover, we discuss the solitary-wave solutions for equations with vanishing potential, space-quadratic potential and optical lattice potential, which are applied to many branches of physics.

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