Modulational Instability and Stationary Waves for the Coupled Generalized Schrödinger-Boussinesq System

2011 ◽  
Vol 66 (3-4) ◽  
pp. 143-150 ◽  
Author(s):  
Zu-Feng Liang
Keyword(s):  
Modulational Instability ◽  
Low Frequency ◽  
Travelling Wave ◽  
Boussinesq System ◽  
Wave Number ◽  
Dispersive Media ◽  
Stationary Waves ◽  
Travelling Wave Solutions ◽  
Frequency Wave ◽  
General Dispersion

The coupled generalized Schr¨odinger-Boussinesq (SB) system, which can describe a highfrequency mode coupled to a low-frequency wave in dispersive media is investigated. First, we study the modulational instability (MI) of the SB system. As a result, the general dispersion relation between the frequency and the wave number of the modulating perturbations is derived, and thus a number of possible MI regions are identified. Then two classes of exact travelling wave solutions are obtained expressed in the general forms. Several explicit examples are presented.

Sources of primary and secondary microseisms

1994 ◽  
Vol 84 (1) ◽  
pp. 142-148
Author(s):  
Robert K. Cessaro
Keyword(s):  
Seismic Noise ◽  
Low Frequency ◽  
Seismic Array ◽  
Wave Number ◽  
Ocean Bottom ◽  
Wide Angle ◽  
Frequency Wave ◽  
Long Period ◽  
Seismic Records ◽  
Near Shore

Abstract Low-frequency (0.01 to 0.2 Hz) seismic noise, arising from pelagic storms, is commonly observed as microseisms in seismic records from land and ocean bottom detectors. One principal research objective, in the study of microseisms, has been to locate their sources. This article reports on an analysis of primary and secondary microseisms (i.e., near and double the frequency of ocean swell) recorded simultaneously on three land-based long-period arrays (Alaskan Long Period Array, Montana Large Aperture Seismic Array, and Norwegian Seismic Array) during the early 1970s. Reliable microseism source locations are determined by wide-angle triangulation, using the azimuths of approach obtained from frequency-wave number analysis of the records of microseisms propagating across these arrays. Two near-shore sources of both primary and secondary microseisms appear to be persistent in the sense that they are associated with essentially constant near-shore locations. Secondary microseisms are observed to emanate from wide-ranging pelagic locations in addition to the same near-shore locations determined for the primary microseisms.

scholarly journals Stability Analysis, Numerical and Exact Solutions of the (1+1)-Dimensional NDMBBM Equation

2018 ◽  
Vol 22 ◽  
pp. 01064 ◽  
Author(s):  
Asif Yokus ◽  
Tukur Abdulkadir Sulaiman ◽  
Mehmet Tahir Gulluoglu ◽  
Hasan Bulut
Keyword(s):  
Gordon Equation ◽  
Travelling Wave ◽  
Wave Transformation ◽  
Dispersive Media ◽  
Travelling Wave Solutions ◽  
New Approach ◽  
Analytical Technique ◽  
Function Solution ◽  
Forward Difference ◽  
Trigonometric Function Solution

A newly propose mathematical approach is presented in this study. We utilize the new approach in investigating the solutions of the (1+1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation. The new analytical technique is based on the popularly known sinh-Gordon equation and a wave transformation. In developing this new technique at each every steps involving integration, the integration constants are considered to not be zero which gives rise to new form of travelling wave solutions. The (1+1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony is used in modelling an approximation for surface long waves in nonlinear dispersive media. We construct some new trigonometric function solution to this equation. Moreover, the finite forward difference method is utilized in investigating the numerical behavior of this equation by taking one of the obtained analytical solutions into consideration. We finally, give a comprehensive conclusions.

scholarly journals Travelling Wave Solutions of the Schrödinger-Boussinesq System

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Adem Kılıcman ◽  
Reza Abazari
Keyword(s):  
Soliton Solutions ◽  
Expansion Method ◽  
Travelling Wave ◽  
Trigonometric Function ◽  
Boussinesq System ◽  
Hyperbolic Function ◽  
Travelling Wave Solutions ◽  
Physical Problems ◽  
Hyperbolic Function Solutions ◽  
Trigonometric Function Solutions

We establish exact solutions for the Schrödinger-Boussinesq Systemiut+uxx−auv=0,vtt−vxx+vxxxx−b(|u|2)xx=0, whereaandbare real constants. The (G′/G)-expansion method is used to construct exact periodic and soliton solutions of this equation. Our work is motivated by the fact that the (G′/G)-expansion method provides not only more general forms of solutions but also periodic and solitary waves. As a result, hyperbolic function solutions and trigonometric function solutions with parameters are obtained. These solutions may be important and of significance for the explanation of some practical physical problems.

scholarly journals North Atlantic Multidecadal Variability Enhancing Decadal Extratropical Extremes in Boreal Late Summer in the Early Twenty-First Century

2020 ◽  
Vol 33 (14) ◽  
pp. 6047-6064 ◽  
Author(s):  
Jie Zhang ◽  
Zhiheng Chen ◽  
Haishan Chen ◽  
Qianrong Ma ◽  
Asaminew Teshome
Keyword(s):  
Energy Transfer ◽  
North Atlantic ◽  
Low Frequency ◽  
Late Summer ◽  
First Century ◽  
Stationary Waves ◽  
Frequency Wave ◽  
Multidecadal Variability ◽  
Longitudinal Temperature Gradient ◽  
Twenty First Century

AbstractIn the beginning of the twenty-first century, weather and climate extremes occurred more and more in extratropical summer, linked to the magnified amplitudes of quasi-stationary waves and external forcing. The study analyzes the relations between multidecadal extratropical extremes in boreal late summer and the North Atlantic (NA; 35°–65°N, 40°W–0°) multidecadal variability (NAMV) in the mid- to high latitudes. The results show that multidecadal extratropical extremes link with the intensified NAMV and the related positive–negative–positive (+ − +) zonal mode of sea surface temperature (SST). 1) The SST mode favors the eastward shift of the negative-phase NA oscillation (NNAO), with a latitudinal pattern of cyclone anomalies over the western European coast and anticyclones over Greenland; NNAO is helpful to baroclinic energy transfer and a longitudinal wavelike pattern. 2) The SST mode and the eddy-driven jet of NNAO are conducive to a southeast extension of the NA jet in close conjunction with the Afro-Asian jet, thereby enhancing the jet waveguide and barotropic energy transfer for the maintenance of a low-frequency wave. 3) The effect of the intensified NAMV on warming Europe contributes to the longitudinal temperature gradient–like “cooling ocean and warming land” pattern, which enhances the meridional wind and wave amplitude of the low-frequency wave. Based on these causes, the intensified NAMV and the + − + SST mode favor the enhancement of the low-frequency wave and quasi-resonant probability, which magnifies the amplitude of the quasi-stationary wave and enhances extratropical extremes on the decadal time scale.

scholarly journals Baroclinic Stationary Waves in Aquaplanet Models

2011 ◽  
Vol 68 (5) ◽  
pp. 1023-1040 ◽  
Author(s):  
Giuseppe Zappa ◽  
Valerio Lucarini ◽  
Antonio Navarra
Keyword(s):  
Dispersion Relation ◽  
Baroclinic Instability ◽  
Surface Wind ◽  
Low Frequency ◽  
Phase Speed ◽  
Stationary Wave ◽  
Instability Wave ◽  
Stationary Waves ◽  
Frequency Wave ◽  
Inverse Energy Cascade

Abstract An aquaplanet model is used to study the nature of the highly persistent low-frequency waves that have been observed in models forced by zonally symmetric boundary conditions. Using the Hayashi spectral analysis of the extratropical waves, the authors find that a quasi-stationary wave 5 belongs to a wave packet obeying a well-defined dispersion relation with eastward group velocity. The components of the dispersion relation with k ≥ 5 baroclinically convert eddy available potential energy into eddy kinetic energy, whereas those with k < 5 are baroclinically neutral. In agreement with Green’s model of baroclinic instability, wave 5 is weakly unstable, and the inverse energy cascade, which had been previously proposed as a main forcing for this type of wave, only acts as a positive feedback on its predominantly baroclinic energetics. The quasi-stationary wave is reinforced by a phase lock to an analogous pattern in the tropical convection, which provides further amplification to the wave. It is also found that the Pedlosky bounds on the phase speed of unstable waves provide guidance in explaining the latitudinal structure of the energy conversion, which is shown to be more enhanced where the zonal westerly surface wind is weaker. The wave’s energy is then trapped in the waveguide created by the upper tropospheric jet stream. In agreement with Green’s theory, as the equator-to-pole SST difference is reduced, the stationary marginally stable component shifts toward higher wavenumbers, while wave 5 becomes neutral and westward propagating. Some properties of the aquaplanet quasi-stationary waves are found to be in interesting agreement with a low frequency wave observed by Salby during December–February in the Southern Hemisphere so that this perspective on low frequency variability, apart from its value in terms of basic geophysical fluid dynamics, might be of specific interest for studying the earth’s atmosphere.

scholarly journals Modulational instability in the full-dispersion Camassa–Holm equation

2017 ◽  
Vol 473 (2203) ◽  
pp. 20170153 ◽  
Author(s):  
Vera Mikyoung Hur ◽  
Ashish Kumar Pandey
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Modulational Instability ◽  
Travelling Wave ◽  
Wave Number ◽  
Stokes Wave ◽  
Holm Equation ◽  
Stability And Instability ◽  
The Stability ◽  
Whitham Equation

We determine the stability and instability of a sufficiently small and periodic travelling wave to long-wavelength perturbations, for a nonlinear dispersive equation which extends a Camassa–Holm equation to include all the dispersion of water waves and the Whitham equation to include nonlinearities of medium-amplitude waves. In the absence of the effects of surface tension, the result qualitatively agrees with the Benjamin–Feir instability of a Stokes wave. In the presence of the effects of surface tension, it qualitatively agrees with those from formal asymptotic expansions of the physical problem and improves upon that for the Whitham equation, predicting the critical wave number at the strong surface tension limit. We discuss the modulational stability and instability in the Camassa–Holm equation and other related models.

Solitary and Travelling Wave Solutions of Certain Nonlinear Diffusion-Reaction Equations

2020 ◽  
Author(s):  
Miftachul Hadi
Keyword(s):  
Nonlinear Diffusion ◽  
Travelling Wave ◽  
Diffusion Reaction ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Reaction Equations

We review the work of Ranjit Kumar, R S Kaushal, Awadhesh Prasad. The work is still in progress.

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