scholarly journals Forced ILW-Burgers Equation as a Model for Rossby Solitary Waves Generated by Topography in Finite Depth Fluids

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Hongwei Yang ◽  
Baoshu Yin ◽  
Yunlong Shi ◽  
Qingbiao Wang
Keyword(s):  
Solitary Waves ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Pseudospectral Method ◽  
Finite Depth ◽  
Perturbation Solution ◽  
Long Waves ◽  
Detuning Parameter ◽  
De Vries ◽  
Rossby Solitary Waves

The paper presents an investigation of the generation, evolution of Rossby solitary waves generated by topography in finite depth fluids. The forced ILW- (Intermediate Long Waves-) Burgers equation as a model governing the amplitude of solitary waves is first derived and shown to reduce to the KdV- (Korteweg-de Vries-) Burgers equation in shallow fluids and BO- (Benjamin-Ono-) Burgers equation in deep fluids. By analysis and calculation, the perturbation solution and some conservation relations of the ILW-Burgers equation are obtained. Finally, with the help of pseudospectral method, the numerical solutions of the forced ILW-Burgers equation are given. The results demonstrate that the detuning parameterαholds important implications for the generation of the solitary waves. By comparing with the solitary waves governed by ILW-Burgers equation and BO-Burgers equation, we can conclude that the solitary waves generated by topography in finite depth fluids are different from that in deep fluids.

scholarly journals A New Integro-Differential Equation for Rossby Solitary Waves with Topography Effect in Deep Rotational Fluids

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Hongwei Yang ◽  
Qingfeng Zhao ◽  
Baoshu Yin ◽  
Huanhe Dong
Keyword(s):  
Differential Equation ◽  
Solitary Waves ◽  
Numerical Solutions ◽  
Kdv Equation ◽  
Pseudospectral Method ◽  
Multiple Scale ◽  
Integro Differential Equation ◽  
Topography Effect ◽  
Detuning Parameter ◽  
Rossby Solitary Waves

From rotational potential vorticity-conserved equation with topography effect and dissipation effect, with the help of the multiple-scale method, a new integro-differential equation is constructed to describe the Rossby solitary waves in deep rotational fluids. By analyzing the equation, some conservation laws associated with Rossby solitary waves are derived. Finally, by seeking the numerical solutions of the equation with the pseudospectral method, by virtue of waterfall plots, the effect of detuning parameter and dissipation on Rossby solitary waves generated by topography are discussed, and the equation is compared with KdV equation and BO equation. The results show that the detuning parameterαplays an important role for the evolution features of solitary waves generated by topography, especially in the resonant case; a large amplitude nonstationary disturbance is generated in the forcing region. This condition may explain the blocking phenomenon which exists in the atmosphere and ocean and generated by topographic forcing.

Cylindrical and Spherical Dust-Ion Acoustic Solitary Waves by Damped Korteweg-de Vries-Burgers Equation

2019 ◽  
Vol 49 (5) ◽  
pp. 693-697 ◽  
Author(s):  
Dong-Ning Gao ◽  
Zheng-Rong Zhang ◽  
Jian-Peng Wu ◽  
Dan Luo ◽  
Wen-Shan Duan ◽  
...  
Keyword(s):  
Solitary Waves ◽  
Burgers Equation ◽  
Ion Acoustic Solitary Waves ◽  
Ion Acoustic ◽  
De Vries

scholarly journals Computational and Numerical Solutions for 2+1-Dimensional Integrable Schwarz–Korteweg–de Vries Equation with Miura Transform

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Raghda A. M. Attia ◽  
S. H. Alfalqi ◽  
J. F. Alzaidi ◽  
Mostafa M. A. Khater ◽  
Dianchen Lu
Keyword(s):  
Solitary Waves ◽  
Decomposition Method ◽  
Numerical Solutions ◽  
Vries Equation ◽  
Adomian Decomposition Method ◽  
Simplest Equation Method ◽  
Adomian Decomposition ◽  
Tanh Method ◽  
De Vries ◽  
Parameter Values

This paper investigates the analytical, semianalytical, and numerical solutions of the 2+1–dimensional integrable Schwarz–Korteweg–de Vries (SKdV) equation. The extended simplest equation method, the sech-tanh method, the Adomian decomposition method, and cubic spline scheme are employed to obtain distinct formulas of solitary waves that are employed to calculate the initial and boundary conditions. Consequently, the numerical solutions of this model can be investigated. Moreover, their stability properties are also analyzed. The solutions obtained by means of these techniques are compared to unravel relations between them and their characteristics illustrated under the suitable choice of the parameter values.

Cylindrical Magnetosonic Solitary Waves by Modified Korteweg–de Vries–Burgers Equation in Electron–Positron–Ion Plasma

2020 ◽  
Vol 46 (2) ◽  
pp. 189-194
Author(s):  
D.-N. Gao ◽  
J.-P. Wu ◽  
Z.-R. Zhang ◽  
D. Luo ◽  
S.-M. Lin ◽  
...  
Keyword(s):  
Solitary Waves ◽  
Burgers Equation ◽  
Ion Plasma ◽  
Electron Positron ◽  
De Vries

scholarly journals Numerical Solutions of the Forced Korteweg-de Vries-Burgers Equation

2019 ◽  
Vol 14 (12) ◽  
pp. 4204-4211
Author(s):  
K.G. Tay ◽  
W.K. Tiong ◽  
Y.Y. Choy ◽  
C.T. Ong
Keyword(s):  
Numerical Solutions ◽  
Burgers Equation ◽  
De Vries

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 Spectrally accurate approximate solutions and convergence analysis of fractional Burgers’ equation

2020 ◽  
Vol 9 (3) ◽  
pp. 633-644
Author(s):  
A. K. Mittal
Keyword(s):  
Numerical Solutions ◽  
Burgers Equation ◽  
Numerical Technique ◽  
Time Derivative ◽  
Pseudospectral Method ◽  
Approximate Solutions ◽  
Algebraic Equations ◽  
Time And Space ◽  
Time Space ◽  
Coupled Burgers Equation

Abstract In this paper, a new numerical technique implements on the time-space pseudospectral method to approximate the numerical solutions of nonlinear time- and space-fractional coupled Burgers’ equation. This technique is based on orthogonal Chebyshev polynomial function and discretizes using Chebyshev–Gauss–Lobbato (CGL) points. Caputo–Riemann–Liouville fractional derivative formula is used to illustrate the fractional derivatives matrix at CGL points. Using the derivatives matrices, the given problem is reduced to a system of nonlinear algebraic equations. These equations can be solved using Newton–Raphson method. Two model examples of time- and space-fractional coupled Burgers’ equation are tested for a set of fractional space and time derivative order. The figures and tables show the significant features, effectiveness, and good accuracy of the proposed method.

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