scholarly journals Finite-amplitude solitary waves at the interface between two homogeneous fluids

1988 ◽  
Vol 31 (12) ◽  
pp. 3550 ◽  
Author(s):  
D. I. Pullin ◽  
R. H. J. Grimshaw
Keyword(s):  
Solitary Waves ◽  
Finite Amplitude

Solitary waves in a dusty adiabatic electronegative plasma

2010 ◽  
Vol 76 (3-4) ◽  
pp. 409-418 ◽  
Author(s):  
A. A. MAMUN ◽  
K. S. ASHRAFI ◽  
M. G. M. ANOWAR
Keyword(s):  
Solitary Waves ◽  
Vries Equation ◽  
Negative Ions ◽  
Finite Amplitude ◽  
Reductive Perturbation Method ◽  
Charged Dust ◽  
Electronegative Plasma ◽  
Ion Acoustic ◽  
Basic Features ◽  
Electronegative Plasmas

AbstractThe dust ion-acoustic solitary waves (SWs) in an unmagnetized dusty adiabatic electronegative plasma containing inertialess adiabatic electrons, inertial single charged adiabatic positive and negative ions, and stationary arbitrarily (positively and negatively) charged dust have been theoretically studied. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation which admits an SW solution. The combined effects of the adiabaticity of plasma particles, inertia of positive or negative ions, and presence of positively or negatively charged dust, which are found to significantly modify the basic features of small but finite-amplitude dust-ion-acoustic SWs, are explicitly examined. The implications of our results in space and laboratory dusty electronegative plasmas are briefly discussed.

The effect of weak shear on finite-amplitude internal solitary waves

1999 ◽  
Vol 395 ◽  
pp. 125-159 ◽  
Author(s):  
S. R. CLARKE ◽  
R. H. J. GRIMSHAW
Keyword(s):  
Evolution Equation ◽  
Solitary Waves ◽  
Vries Equation ◽  
Physical Space ◽  
Finite Amplitude ◽  
Initial Condition ◽  
Weak Current ◽  
Inflection Points ◽  
Wide Range ◽  
De Vries

A finite-amplitude long-wave equation is derived to describe the effect of weak current shear on internal waves in a uniformly stratified fluid. This effect is manifested through the introduction of a nonlinear term into the amplitude evolution equation, representing a projection of the shear from physical space to amplitude space. For steadily propagating waves the evolution equation reduces to the steady version of the generalized Korteweg–de Vries equation. An analysis of this equation is presented for a wide range of possible shear profiles. The type of waves that occur is found to depend on the number and position of the inflection points of the representation of the shear profile in amplitude space. Up to three possible inflection points for this function are considered, resulting in solitary waves and kinks (dispersionless bores) which can have up to three characteristic lengthscales. The stability of these waves is generally found to decrease as the complexity of the waves increases. These solutions suggest that kinks and solitary waves with multiple lengthscales are only possible for shear profiles (in physical space) with a turning point, while instability is only possible if the shear profile has an inflection point. The unsteady evolution of a periodic initial condition is considered and again the solution is found to depend on the inflection points of the amplitude representation of the shear profile. Two characteristic types of solution occur, the first where the initial condition evolves into a train of rank-ordered solitary waves, analogous to those generated in the framework of the Korteweg–de Vries equation, and the second where two or more kinks connect regions of constant amplitude. The unsteady solutions demonstrate that finite-amplitude effects can act to halt the critical collapse of solitary waves which occurs in the context of the generalized Korteweg–de Vries equation. The two types of solution are then used to qualititatively relate previously reported observations of shock formation on the internal tide propagating onto the Australian North West Shelf to the observed background current shear.

scholarly journals From non-local gap solitary waves to bound states in periodic media

2011 ◽  
Vol 468 (2137) ◽  
pp. 116-135 ◽  
Author(s):  
T. R. Akylas ◽  
Guenbo Hwang ◽  
Jianke Yang
Keyword(s):  
Solitary Waves ◽  
Bound States ◽  
Wave Spectrum ◽  
Separation Distance ◽  
Finite Amplitude ◽  
Linear Wave ◽  
Periodic Media ◽  
Non Local ◽  
Gap Solitons ◽  
Power Curves

Solitary waves in one-dimensional periodic media are discussed by employing the nonlinear Schrödinger equation with a spatially periodic potential as a model. This equation admits two families of gap solitons that bifurcate from the edges of Bloch bands in the linear wave spectrum. These fundamental solitons may be positioned only at specific locations relative to the potential; otherwise, they become non-local owing to the presence of growing tails of exponentially small amplitude with respect to the wave peak amplitude. Here, by matching the tails of such non-local solitary waves, high-order locally confined gap solitons, or bound states, are constructed. Details are worked out for bound states comprising two non-local solitary waves in the presence of a sinusoidal potential. A countable set of bound-state families, characterized by the separation distance of the two solitary waves, is found, and each family features three distinct solution branches that bifurcate near Bloch-band edges at small, but finite, amplitude. Power curves associated with these solution branches are computed asymptotically for large solitary-wave separation, and the theoretical predictions are consistent with numerical results.

Nonlinear propagation of dust-ion-acoustic solitary waves in an unmagnetized dusty plasma with trapped particle distribution

2015 ◽  
Vol 30 (40) ◽  
pp. 1550216 ◽  
Author(s):  
O. Rahman
Keyword(s):  
Dusty Plasma ◽  
Solitary Waves ◽  
Perturbation Technique ◽  
Negative Ions ◽  
Mkdv Equation ◽  
Finite Amplitude ◽  
Negative Ion ◽  
Nonlinear Propagation ◽  
Ion Distribution ◽  
Ion Acoustic

The nonlinear propagation of dust-ion-acoustic (DIA) solitary waves (SWs) in an unmagnetized four-component dusty plasma containing electrons and negative ions obeying vortex-like (trapped) velocity distribution, cold mobile positive ions and arbitrarily charged stationary dust has been theoretically investigated. The properties of small but finite amplitude DIASWs are studied by employing the reductive perturbation technique. It has been found that owing to the departure from the Maxwellian electron and Maxwellian negative ion distribution to a vortex-like one, the dynamics of such DIASWs is governed by a modified Korteweg–de Vries (mKdV) equation which admits SW solution under certain conditions. The basic properties (speed, amplitude, width, etc.) of such DIASWs are found to be significantly modified by the presence of trapped electron and trapped negative ions. The implications of our results to space and laboratory dusty electronegative plasmas (DENPs) are briefly discussed.

MATHEMATICAL MODELING OF THERMOGASDYNAMIC PROCESSES IN PISTON ENGINES

2021 ◽  
pp. 12-17
Author(s):  
A. N. Berdnik ◽  
V. O. Remeslovskiy
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Solitary Waves ◽  
Gas Flow ◽  
Method Of Characteristics ◽  
Finite Amplitude ◽  
Piston Engine ◽  
The Method Of Characteristics ◽  
Turbocharging System ◽  
Calculation Results

A method for calculating the non-stationary gas flow in the exhaust pipeline of a piston engine by the method of solitary waves of finite amplitude is presented. The comparison of experimental data and calculation results by the method of characteristics and obtained when considering the process of propagation of solitary waves through the exhaust pipeline of a piston engine equipped with a pulsed turbocharging system is shown.

Localized finite-amplitude disturbances and selection of solitary waves

2000 ◽  
Vol 62 (4) ◽  
pp. 4959-4962 ◽  
Author(s):  
I. L. Kliakhandler ◽  
A. V. Porubov ◽  
M. G. Velarde
Keyword(s):  
Solitary Waves ◽  
Finite Amplitude ◽  
Selection Of

Modulations of slow sausage surface waves travelling along a magnetized slab

1994 ◽  
Vol 51 (2) ◽  
pp. 291-308 ◽  
Author(s):  
I. Zhelyazko ◽  
K. Murawski ◽  
M. Goossens ◽  
P. Nenovaki ◽  
B. Roberts
Keyword(s):  
Asymptotic Expansion ◽  
Surface Wave ◽  
Solitary Waves ◽  
Amplitude Modulation ◽  
Finite Amplitude ◽  
Mhd Equations ◽  
Periodic Waves ◽  
Initial States ◽  
Cubic Nonlinear Schrödinger Equation ◽  
Free Interfaces

In this paper we consider a set of nonlinear MHD equations that admits in a linear approximation a solution in the form of a slow sausage surface wave travelling along an isolated magnetic slab. For a wave of small but finite amplitude, we investigate how a slowly varying amplitude is modulated by nonlinear self-interactions. A stretching transformation shows that, at the lowest order of an asymptotic expansion, the original set of equations with appropriate boundary conditions (free interfaces) can be reduced to the cubic nonlinear Schrödinger equation, which determines the amplitude modulation. We study analytically and numerically the evolution of impulsively generated waves, showing a transition of the initial states into a train of solitons and periodic waves. The possibility of the existence of solitary waves in the solar atmosphere is also briefly discussed.

Nonlinear evolution of waves on a vertically falling film

1993 ◽  
Vol 250 ◽  
pp. 433-480 ◽  
Author(s):  
H.-C. Chang ◽  
E. A. Demekhin ◽  
D. I. Kopelevich
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Travelling Wave ◽  
Finite Amplitude ◽  
Capillary Waves ◽  
Stationary Waves ◽  
Falling Film ◽  
Linear Mode

Wave formation on a falling film is an intriguing hydrodynamic phenomenon involving transitions among a rich variety of spatial and temporal structures. Immediately beyond an inception region, short, near-sinusoidal capillary waves are observed. Further downstream, long, near-solitary waves with large tear-drop humps preceded by short, front-running capillary waves appear. Both kinds of waves evolve slowly downstream such that over about ten wavelengths, they resemble stationary waves which propagate at constant speeds and shapes. We exploit this quasi-steady property here to study wave evolution and selection on a vertically falling film. All finite-amplitude stationary waves with the same average thickness as the Nusselt flat film are constructed numerically from a boundary-layer approximation of the equations of motion. As is consistent with earlier near-critical analyses, two travelling wave families are found, each parameterized by the wavelength or the speed. One family γ1travels slower than infinitesimally small waves of the same wavelength while the other family γ2and its hybrids travel faster. Stability analyses of these waves involving three-dimensional disturbances of arbitrary wavelength indicate that there exists a unique nearly sinusoidal wave on the slow family γ1with wavenumber αs(or α2) that has the lowest growth rate. This wave is slightly shorter than the fastest growing linear mode with wavenumber αmand approaches the wave on γ1with the highest flow rate at low Reynolds numbers. On the fast γ2family, however, multiple bands of near-solitary waves bounded below by αfare found to be stable to two-dimensional disturbances. This multiplicity of stable bands can be interpreted as a result of favourable interaction among solitary-wave-like coherent structures to form a periodic train. (All waves are unstable to three-dimensional disturbances with small growth rates.) The suggested selection mechanism is consistent with literature data and our numerical experiments that indicate waves slow down immediately beyond inception as they approach the short capillary wave with wavenumber α2of the slow γ1family. They then approach the long stable waves on the γ2family further downstream and hence accelerate and develop into the unique solitary wave shapes, before they succumb to the slowly evolving transverse disturbances.

scholarly journals Characterization and dynamical stability of fully nonlinear strain solitary waves in a fluid-filled hyperelastic membrane tube

2020 ◽  
Vol 231 (10) ◽  
pp. 4095-4110 ◽  
Author(s):  
A. T. Il’íchev ◽  
V. A. Shargatov ◽  
Y. B. Fu
Keyword(s):  
Solitary Waves ◽  
Wave Speed ◽  
Finite Amplitude ◽  
Quiescent State ◽  
Governing Equations ◽  
Membrane Tube ◽  
Stability Of Solitary Waves ◽  
The Stability ◽  
Intermediate Value

Abstract We first characterize strain solitary waves propagating in a fluid-filled membrane tube when the fluid is stationary prior to wave propagation and the tube is also subjected to a finite stretch. We consider the parameter regime where all traveling waves admitted by the linearized governing equations have nonzero speed. Solitary waves are viewed as waves of finite amplitude that bifurcate from the quiescent state of the system with the wave speed playing the role of the bifurcation parameter. Evolution of the bifurcation diagram with respect to the pre-stretch is clarified. We then study the stability of solitary waves for a representative case that is likely of most interest in applications, the case in which solitary waves exist with speed c lying in the interval $$[0, c_1)$$ [ 0 , c 1 ) where $$c_1$$ c 1 is the bifurcation value of c, and the wave amplitude is a decreasing function of speed. It is shown that there exists an intermediate value $$c_0$$ c 0 in the above interval such that solitary waves are spectrally stable if their speed is greater than $$c_0$$ c 0 and unstable otherwise.

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