Numerical simulation of coupled long wave-short wave system with a mismatch in group velocities

2005 ◽  
Author(s):  
Chun-Kin Poon
Keyword(s):  
Numerical Simulation ◽  
Short Wave ◽  
Wave System ◽  
Long Wave ◽  
Group Velocities

scholarly journals The amplitude system for a Simultaneous short-wave Turing and long-wave Hopf instability

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Guido Schneider ◽  
Matthias Winter
Keyword(s):  
Numerical Simulation ◽  
Analytical Approach ◽  
Reaction Diffusion ◽  
Short Wave ◽  
Reaction Diffusion Systems ◽  
Long Wave ◽  
Diffusion Systems ◽  
Schnakenberg Model ◽  
Pattern Forming ◽  
Amplitude System

<p style='text-indent:20px;'>We consider reaction-diffusion systems for which the trivial solution simultaneously becomes unstable via a short-wave Turing and a long-wave Hopf instability. The Brusseletor, Gierer-Meinhardt system and Schnakenberg model are prototype biological pattern forming systems which show this kind of behavior for certain parameter regimes. In this paper we prove the validity of the amplitude system associated to this kind of instability. Our analytical approach is based on the use of mode filters and normal form transformations. The amplitude system allows us an efficient numerical simulation of the original multiple scaling problems close to the instability.</p>

Influence of contact loss underneath concrete underlayer on dynamic performance of prefabricated concrete slab track

2016 ◽  
Vol 231 (3) ◽  
pp. 345-358 ◽  
Author(s):  
Ren Juanjuan ◽  
Yang Rongshan ◽  
Wang Ping ◽  
Dai Feng ◽  
Yan Xiaobo
Keyword(s):  
Numerical Simulation ◽  
Dynamic Response ◽  
High Speed ◽  
Critical Value ◽  
Short Wave ◽  
Dominant Factor ◽  
Track Structure ◽  
Slab Track ◽  
Actual Contact ◽  
Long Wave

Contact loss between the concrete underlayer and the subgrade caused by the differential settlement or stiffness of subgrade structure is a common distress, which deteriorates the mechanical properties of the track structure and adversely affects the safety and comfort for the operation on high-speed railway. The objective of this paper is to study the damage mechanism of prefabricated slab track subjected to such contact loss and to propose a critical value for the size of contact loss that would not jeopardize the safety of rail traffic and riding comfort of passengers. Thus, a vibration calculation model for the vertically coupled vehicle-J-slab track-subgrade system is established using finite element method, both of the short-wave irregularity and the German long-wave irregularity were taken into account to calculate the dynamic response of vehicle, track structure and subgrade with different contact loss areas and speeds scenarios. Based on the numerical simulation results, a critical value of contact loss area is proposed. When the actual contact loss area is smaller than the critical value, the welded joint irregularity is the dominant factor in the vehicle dynamic response; however, when the actual contact loss area is larger than the critical value, the track irregularity induced by contact loss under the concrete underlayer becomes the dominant factor. It is suggested that the contact loss area should be controlled under the critical value in order to ease or mitigate the dynamic response of the vehicle and track structure. The numerical simulation indicates the critical contact loss area is about 10 m2 for the short-wave irregularity case and 14 m2 for the long-wave irregularity case, thus it is suggested that the contact loss area underneath the concrete underlayer should not exceed 10 m2, which is consistent with the Swedish standard and the German standard on weak areas of subgrade compaction.

scholarly journals NUMERICAL SIMULATION OF IRREGULAR BIMODAL WAVE SYSTEM DYNAMICS WITHIN THE FRAMEWORK OF KORTEWEG-DE VRIES EQUATION

2019 ◽  
Vol 47 (1) ◽  
pp. 38-40
Author(s):  
E.G. Didenkulova ◽  
A.V. Slunyaev ◽  
E.N. Pelinovsky
Keyword(s):  
Numerical Simulation ◽  
Shallow Water ◽  
Vries Equation ◽  
Kdv Equation ◽  
Wave Spectrum ◽  
Wave System ◽  
Quasi Equilibrium ◽  
Long Wave ◽  
De Vries ◽  
The Waves

The dynamics of wave ensembles in shallow water is studied within the framework of the nonlinear dispersive Korteweg – de Vries (KdV) equation by numerical simulation. Bimodal wave systems whose energy is distributed over two spectral domains are considered: the “additional” lobe which corresponds to the system of longer or shorter waves is added to the “main” spectral peak. The concerned problem describes, for example, the interaction between wind waves and swell in shallow water. The case of the unimodal waves (considered in (Pelinovsky, Sergeeva, 2006) is used as the reference. The limitations of the implied assumptions and the relationship of the idealized model to the realistic conditions in the ocean were discussed in the recent paper (Wang et al, 2018). Based on the detailed consideration of the 6 simulated cases, the following general conclusions may be formulated. The transition from the initial state to the quasi-equilibrium one is accompanied by strong variations of the wave characteristics, when the waves exhibit the most extreme features. In particular, the wave kurtosis grows suddenly and the abnormal heavy tails in the wave amplitude probability distributions appear. These processes are observed in all the cases of the bimodal spectra and are quite similar to the single-mode regime. The coexistence of a long-wave system smoothens the rapid oscillations of the wave extremes and kurtosis which take place during the transition stage. The presence of a short-wave system makes the waves on average more symmetric. Skewness attains the minimum value compared to the other cases. The co-existence of shorter waves practically does not change the wave kurtosis or the probability of the wave heights. In contrast, the presence of a long-wave system makes the waves more asymmetric and more extreme. The probability of large waves increases in the bimodal systems with a low-frequency component. The initial wave spectrum expands as a result of the wave interaction and tends to a quasistationary state. One may anticipate that the formulated conclusions are applicable beyond the limits of the Korteweg-de Vries equation to other kindred frameworks and corresponding phenomena. This work was supported by the Russian Science Foundation (project No. 18-77-00063).

scholarly journals Soliton, Breather-Like and Dark-Soliton-Breather-Like Solutions for the Coupled Long-Wave-Short-Wave System

2021 ◽  
Author(s):  
Kuai Bi ◽  
Hui-Qin Hao ◽  
Jian-Wen Zhang ◽  
Rui Guo
Keyword(s):  
Asymptotic Analysis ◽  
Dark Soliton ◽  
Short Wave ◽  
Wave System ◽  
Hirota Bilinear Method ◽  
Analysis Method ◽  
Bilinear Method ◽  
Long Wave ◽  
Different Types ◽  
Hirota Bilinear

Abstract In this paper, we will obtain the exact $N$-soliton solution of the coupled long-wave-short-wave system via the developed Hirota bilinear method. Through manipulating the relevant parameters, we will construct different types of solutions which include breather-like solutions and dark-soliton-breather-like solutions. Moreover, we will demonstrate that the interactions of two-soliton and two-breather-like solutions are all elastic through asymptotic analysis method. Finally, we will display the interactions through illustrations.PACS 05.45.Yv; 02.30.Ik; 42.81.Dp

scholarly journals Mixed solitons in a (2+1)-dimensional multicomponent long-wave–short-wave system

2014 ◽  
Vol 90 (4) ◽  
Author(s):  
T. Kanna ◽  
M. Vijayajayanthi ◽  
M. Lakshmanan
Keyword(s):  
Short Wave ◽  
Wave System ◽  
Long Wave
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