scholarly journals Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer Fluids

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 41 ◽  
Author(s):  
Lei Fu ◽  
Yaodeng Chen ◽  
Hongwei Yang
Keyword(s):  
Rossby Waves ◽  
Expansion Method ◽  
Weakly Nonlinear ◽  
Multi Scale ◽  
Coupled Equations ◽  
Time Space ◽  
Weakly Nonlinear Waves ◽  
Waves Interaction ◽  
Geostrophic Vortex ◽  
First Time

In this paper, the theoretical model of Rossby waves in two-layer fluids is studied. A single quasi-geostrophic vortex equation is used to derive various models of Rossby waves in a one-layer fluid in previous research. In order to explore the propagation and interaction of Rossby waves in two-layer fluids, from the classical quasi-geodesic vortex equations, by employing the multi-scale analysis and turbulence method, we derived a new (2+1)-dimensional coupled equations set, namely the generalized Zakharov-Kuznetsov(gZK) equations set. The gZK equations set is an extension of a single ZK equation; they can describe two kinds of weakly nonlinear waves interaction by multiple coupling terms. Then, for the first time, based on the semi-inverse method and the variational method, a new fractional-order model which is the time-space fractional coupled gZK equations set is derived successfully, which is greatly different from the single fractional equation. Finally, group solutions of the time-space fractional coupled gZK equations set are obtained with the help of the improved ( G ′ / G ) -expansion method.

Solitary waves under curved topography and beta approximation

2020 ◽  
Vol 34 (17) ◽  
pp. 2050196
Author(s):  
Jiaqi Zhang ◽  
Liangui Yang ◽  
Ruigang Zhang
Keyword(s):  
Solitary Waves ◽  
Wave Amplitude ◽  
Rossby Waves ◽  
Perturbation Expansion ◽  
Expansion Method ◽  
Qualitative And Quantitative Analysis ◽  
Qualitative And Quantitative ◽  
Time Space ◽  
First Time ◽  
Perturbation Expansion Method

In this paper, the mechanisms of excitation and propagation of nonlinear Rossby waves are investigated by the approach of topographic balance under the beta approximation for the first time. Using time-space elongation transformation and perturbation expansion method, a Korteweg–de Vries model equation for topographic Rossby wave amplitude is derived. The influences of topography parameters on Rossby solitary waves are discussed through qualitative and quantitative analysis.

Exact soliton solutions for the interaction of few-cycle-pulse with nonlinear medium

2016 ◽  
Vol 30 (28n29) ◽  
pp. 1640013 ◽  
Author(s):  
Bang-Xing Guo ◽  
Ji Lin
Keyword(s):  
Nonlinear Medium ◽  
Soliton Solutions ◽  
Wave Interaction ◽  
Expansion Method ◽  
Periodic Wave ◽  
Interaction Solution ◽  
Coupled Equations ◽  
Waves Interaction ◽  
The One ◽  
Cycle Pulse

We study the Panilevé property of the coupled equations describing the interaction of few-cycle-pulse with nonlinear medium. And we use the consistent tanh expansion (CTE) method to search for exact interaction soliton solutions of the coupled equations. Many interaction solutions are obtained, such as the one kink-one periodic wave interaction solution, one kink-two periodic waves interaction solution, one kink-one dipole soliton interaction solution, one kink-two dipole solitons interaction solution, and one kink-soliton-one periodic wave interaction solution. We also obtain the kink–kink interaction by using Painlevé truncated expansion method.

scholarly journals A forced 3-D time fractional ZK-Burgers model for Rossby solitary waves with dissipation and thermal forcing

2019 ◽  
Vol 23 (3 Part A) ◽  
pp. 1689-1695 ◽  
Author(s):  
Lei Fu ◽  
Zheyuan Yu ◽  
Huanhe Dong ◽  
Yuqing Li ◽  
Hongwei Yang
Keyword(s):  
Fractional Derivative ◽  
Solitary Waves ◽  
Rossby Waves ◽  
Burgers Equation ◽  
Expansion Method ◽  
Scale Analysis ◽  
Thermal Forcing ◽  
Multi Scale ◽  
Rossby Solitary Waves ◽  
Multi Scale Analysis

In the paper, beginning from the quasi-geostrophic potential vorticity equation with the dissipation and thermal forcing in stratified fluid, by employing multi-scale analysis and perturbation method, we derive a forced 3-D Zakharov Kuznetsor (ZK)-Burgers equation describe the propagation of the Rossby solitary waves within the fractional derivative. The exact solutions are given by virtue of the (G?/G)-expansion method to analyze the excitation effect of thermal forcing on the Rossby waves.

scholarly journals Bragg Resonance around the Coast of Hardwall

2016 ◽  
Vol 7 (4) ◽  
pp. 275
Author(s):  
Viska Noviantri ◽  
Ro’fah Nur Rachmawati
Keyword(s):  
Wave Length ◽  
Expansion Method ◽  
Wave Transmission ◽  
Bragg Resonance ◽  
Incoming Wave ◽  
Approximation Solution ◽  
Multi Scale ◽  
The Right ◽  
Asymptotic Expansion Method ◽  
Transmission And Reflection

Basically, when waves pass an uneven basis, then this wave will be split into transmission and reflection waves. First of all, it will be shown that a sinusoidal seabed can lead to the phenomenon of Bragg resonance. Bragg resonance occurs when the wave-length comes at twice the wave-length of a sinusoidal basis. The method used to obtain approximation solution is a multi-scale asymptotic expansion method. A research on the effect of Bragg resonance on sinusoidal basis had been studied. Sinusoidal basis can reduce the amplitude of the incoming wave so that the amplitude of the wave transmission is quite small. In these researcher, the coast is assumed ideal and can absorb all the energy of the wave transmission. If the beach can reflect waves, this indicates that the existence of sinusoidal basis is more harmful to the coast. This mechanism relies on the distance between the base sinusoidal and beaches. The present research will examined the influence of the base, when there was a beach of hard-wall on the right, which was perfectly capable of reflecting waves. Having regard to the phase difference, from super positioned waves when they hit the beach, so it can determine the safert and the most dangerous distance.

scholarly journals IDENTITY IMPLICATIONS: «FROM THE COUNTRY OF RICE AND OPIUM» BY SOFIIA YABLONSKA

2018 ◽  
Vol 31 ◽  
pp. 251-266
Author(s):  
Tymofii HAVRYLIV
Keyword(s):  
Travel Literature ◽  
Spatial Dimension ◽  
Interdisciplinary Studies ◽  
Complex Nature ◽  
Time Space ◽  
The World ◽  
Self Knowledge ◽  
The Given ◽  
First Time ◽  
Ukrainian Society

This article is one of the first scholarly attempts to analyze the creative work of Ukrainian filmmaker and traveler Sofiia Yablonska-Uden. For the first time in the Ukrainian and the world literary studies, identical implications are analyzed in the «From the Country of Rice and Opium» by S. Yablonska. The purpose of the article is to highlight the complex nature of identity issues in travel literature. In terms of identity, the journey performs two fundamental, closely interconnected tasks: knowledge of the other and self-knowledge. Hermeneutic approaches are used in the article. The main results can be summarized as follows: 1) the journey has its own time-spatial dimension, consisting of two disproportionate moments: preparation for travel and travel itself, and begins literally and symbolically with the overcoming, or the crossing of the border; 2) the intention of the trip contains an identity challenge that affects the preparation, organization, realization of the travel, the way and the content of documenting impressions; 3) such parameters of travel as an accident, an adventure, a game which formed the world of traveler's impressions, are subordinated to the identity problem in the given work; 4) the essay character of the book makes it possible to talk about implications as a response to an identity challenge. The book of travel essays «From the Country of Rice and Opium» of S. Yablonska-Uden is a sample of a successful combination of the business and private aspects of travel, intentions of knowledge and self-knowledge, poetry and faculty; learning about another people and countries, the writer learns a lot of things about himself. Travel literature is an important study object of Ukrainian writing, which opens the prospects for further interdisciplinary studies. The study of travel literature, an identity issue, is extremely relevant both for the development of Ukrainian society and for the formation of optimal responses to the challenges of our time. Keywords travel, travel literature, identity, identical implications, time-space disposition.

scholarly journals Weakly nonlinear waves in magnetized plasma with a slightly non-Maxwellian electron distribution. Part 2. Stability of cnoidal waves

2007 ◽  
Vol 73 (6) ◽  
pp. 933-946
Author(s):  
S. PHIBANCHON ◽  
M. A. ALLEN ◽  
G. ROWLANDS
Keyword(s):  
Growth Rate ◽  
Nonlinear Waves ◽  
Electron Distribution ◽  
Magnetized Plasma ◽  
Weakly Nonlinear ◽  
Long Wavelength ◽  
First Order ◽  
Wave Solutions ◽  
Linear Waves ◽  
Weakly Nonlinear Waves

AbstractWe determine the growth rate of linear instabilities resulting from long-wavelength transverse perturbations applied to periodic nonlinear wave solutions to the Schamel–Korteweg–de Vries–Zakharov–Kuznetsov (SKdVZK) equation which governs weakly nonlinear waves in a strongly magnetized cold-ion plasma whose electron distribution is given by two Maxwellians at slightly different temperatures. To obtain the growth rate it is necessary to evaluate non-trivial integrals whose number is kept to a minimum by using recursion relations. It is shown that a key instance of one such relation cannot be used for classes of solution whose minimum value is zero, and an additional integral must be evaluated explicitly instead. The SKdVZK equation contains two nonlinear terms whose ratio b increases as the electron distribution becomes increasingly flat-topped. As b and hence the deviation from electron isothermality increases, it is found that for cnoidal wave solutions that travel faster than long-wavelength linear waves, there is a more pronounced variation of the growth rate with the angle θ at which the perturbation is applied. Solutions whose minimum values are zero and which travel slower than long-wavelength linear waves are found, at first order, to be stable to perpendicular perturbations and have a relatively narrow range of θ for which the first-order growth rate is not zero.

PROPAGATION OF WEAKLY NONLINEAR WAVES IN A FLUID-FILLED THIN ELASTIC TUBE

1999 ◽  
Vol 23 (2) ◽  
pp. 253-265
Author(s):  
H. Demiray
Keyword(s):  
Nonlinear Waves ◽  
Vries Equation ◽  
Perturbation Technique ◽  
Fluid Pressure ◽  
Static Field ◽  
Elastic Tube ◽  
Inviscid Fluid ◽  
Weakly Nonlinear ◽  
De Vries ◽  
Weakly Nonlinear Waves

In this work, we study the propagation of weakly nonlinear waves in a prestressed thin elastic tube filled with an inviscid fluid. In the analysis, considering the physiological conditions under which the arteries function, the tube is assumed to be subjected to a uniform pressure P0 and a constant axial stretch ratio λz. In the course of blood flow in arteries, it is assumed that a finite time dependent radial displacement is superimposed on this static field but, due to axial tethering, the effect of axial displacement is neglected. The governing nonlinear equation for the radial motion of the tube under the effect of fluid pressure is obtained. Using the exact nonlinear equations of an incompressible inviscid fluid and the reductive perturbation technique, the propagation of weakly nonlinear waves in a fluid-filled thin elastic tube is investigated in the longwave approximation. The governing equation for this special case is obtained as the Korteweg-de-Vries equation. It is shown that, contrary to the result of previous works on the same subject, in the present work, even for Mooney-Rivlin material, it is possible to obtain the nonlinear Korteweg-de-Vries equation.

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