scholarly journals Benjamin-Ono-Burgers-MKdV Equation for Algebraic Rossby Solitary Waves in Stratified Fluids and Conservation Laws

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Hongwei Yang ◽  
Shanshan Jin ◽  
Baoshu Yin
Keyword(s):  
Conservation Laws ◽  
Solitary Waves ◽  
Rossby Waves ◽  
Multiple Scale ◽  
Mkdv Equation ◽  
Center Of Gravity ◽  
Stratified Fluids ◽  
Scale Method ◽  
Small Dissipation ◽  
Rossby Solitary Waves

In the paper, by using multiple-scale method, the Benjamin-Ono-Burgers-MKdV (BO-B-MKdV) equation is obtained which governs algebraic Rossby solitary waves in stratified fluids. This equation is first derived for Rossby waves. By analysis and calculation, some conservation laws are derived from the BO-B-MKdV equation without dissipation. The results show that the mass, momentum, energy, and velocity of the center of gravity of algebraic Rossby waves are conserved and the presence of a small dissipation destroys these conservations.

Slowly varying solitary waves in deep fluids

1981 ◽  
Vol 376 (1765) ◽  
pp. 319-332 ◽  
Keyword(s):  
Solitary Wave ◽  
Asymptotic Solution ◽  
Conservation Laws ◽  
Internal Waves ◽  
Solitary Waves ◽  
Multiple Scale ◽  
Perturbation Parameter ◽  
Fluid Equation ◽  
Scale Method ◽  
Deep Fluid

The slowly varying solitary wave is constructed as an asymptotic solution of the deep fluid equation of Benjamin (1967), Davis & Acrivos (1967), and Ono (1975). A multiple scale method is used to determine the amplitude and phase of the wave to second order in the perturbation parameter. Behind the solitary wave a shelf develops. Outer expansions are intro­duced to remove certain non-uniformities in the expansion. The results are interpreted from conservation laws. Finally the effect of damping, either due to radiating internal waves or due to friction, is considered.

scholarly journals (2 + 1)-Dimensional Coupled Model for Envelope Rossby Solitary Waves and Its Solutions as well as Chirp Effect

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Xin Chen ◽  
Hongwei Yang ◽  
Min Guo ◽  
Baoshu Yin
Keyword(s):  
Solitary Waves ◽  
Rossby Waves ◽  
Modulation Instability ◽  
Multiple Scales ◽  
Coupled Model ◽  
Nls Equation ◽  
Coupled Models ◽  
Trial Function Method ◽  
Rossby Solitary Waves ◽  
Stable Feature

Using the method of multiple scales and perturbation method, a set of coupled models describing the envelope Rossby solitary waves in (2+1)-dimensional condition are obtained, also can be called coupled NLS (CNLS) equations. Following this, based on trial function method, the solutions of the NLS equation are deduced. Moreover, the modulation instability of coupled envelope Rossby waves is studied. We can find that the stable feature of coupled envelope Rossby waves is decided by the value of S. Finally, learning from the concept of chirp in the optical soliton communication field, we study the chirp effect caused by nonlinearity and dispersion in the propagation of Rossby waves.

scholarly journals Rossby Solitary Waves Generated by Wavy Bottom in Stratified Fluids

2013 ◽  
Vol 5 ◽  
pp. 289269 ◽  
Author(s):  
Hongwei Yang ◽  
Baoshu Yin ◽  
Bo Zhong ◽  
Huanhe Dong
Keyword(s):  
Solitary Waves ◽  
Stratified Fluids ◽  
Rossby Solitary Waves

Slowly varying solitary waves. I. Korteweg-de Vries equation

1979 ◽  
Vol 368 (1734) ◽  
pp. 359-375 ◽  
Keyword(s):  
Exact Solution ◽  
Solitary Wave ◽  
Asymptotic Solution ◽  
Solitary Waves ◽  
Variable Coefficient ◽  
Vries Equation ◽  
Multiple Scale ◽  
Perturbation Parameter ◽  
Scale Method ◽  
De Vries

The slowly varying solitary wave is constructed as an asymptotic solution of the variable coefficient Korteweg-de Vries equation. A multiple scale method is used to determine the amplitude and phase of the wave to the second order in the perturbation parameter. The structure ahead and behind the solitary wave is also determined, and the results are interpreted by using conservation laws. Outer expansions are introduced to remove non-uniformities in the expansion. Finally, when the coefficients satisfy a certain constraint, an exact solution is constructed.

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.

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 (2+1)-Dimensional mKdV Hierarchy and Chirp Effect of Rossby Solitary Waves

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Chunlei Wang ◽  
Yong Zhang ◽  
Baoshu Yin ◽  
Xiaoen Zhang
Keyword(s):  
Solitary Wave ◽  
Riccati Equation ◽  
Lie Algebra ◽  
Integrable System ◽  
Solitary Waves ◽  
Mkdv Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Rossby Solitary Waves ◽  
Mkdv Hierarchy

By constructing a kind of generalized Lie algebra, based on generalized Tu scheme, a new (2+1)-dimensional mKdV hierarchy is derived which popularizes the results of (1+1)-dimensional integrable system. Furthermore, the (2+1)-dimensional mKdV equation can be applied to describe the propagation of the Rossby solitary waves in the plane of ocean and atmosphere, which is different from the (1+1)-dimensional mKdV equation. By virtue of Riccati equation, some solutions of (2+1)-dimensional mKdV equation are obtained. With the help of solitary wave solutions, similar to the fiber soliton communication, the chirp effect of Rossby solitary waves is discussed and some conclusions are given.

scholarly journals On Galilean Invariant and Energy Preserving BBM-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 878
Author(s):  
Alexei Cheviakov ◽  
Denys Dutykh ◽  
Aidar Assylbekuly
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Numerical Simulations ◽  
Solitary Waves ◽  
Local Symmetry ◽  
Symmetry And Conservation Laws ◽  
Higher Order ◽  
Special Equation ◽  
Long Wave ◽  
Local Symmetries

We investigate a family of higher-order Benjamin–Bona–Mahony-type equations, which appeared in the course of study towards finding a Galilei-invariant, energy-preserving long wave equation. We perform local symmetry and conservation laws classification for this family of Partial Differential Equations (PDEs). The analysis reveals that this family includes a special equation which admits additional, higher-order local symmetries and conservation laws. We compute its solitary waves and simulate their collisions. The numerical simulations show that their collision is elastic, which is an indication of its S−integrability. This particular PDE turns out to be a rescaled version of the celebrated Camassa–Holm equation, which confirms its integrability.

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