Abstract
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.
Highlights
Nonlinear waves are crucial for the dynamics of the ocean and atmosphere [1,2,3,4]; Rossby waves hold a central position in nonlinear waves
This equation is greatly different from the common equation to describe algebraic Rossby solitary waves, such as the BO equation [10] and the BO-Burgers equation; it includes the dissipation effect and dispersion effect and has stronger nonlinearity
Conservation laws are a common feature of mathematical physics and describe physical properties that remain constant throughout the various processes that occur in the physical world
Summary
Nonlinear waves are crucial for the dynamics of the ocean and atmosphere [1,2,3,4]; Rossby waves hold a central position in nonlinear waves. Much attention has been paid to the Rossby solitary waves. A number of analytical studies of evolution equations governing such waves have been carried out. The aim of the paper is to derive a new equation which governs the behavior of algebraic Rossby solitary waves. From the quasigeostrophic potential vorticity equation in stratified fluids, a new equation (BO-B-MKdV) is generated and is suitable for describing the evolution of Rossby solitary waves. The BO-B-MKdV equation includes dissipation effect and dispersion effect. It is a meaningful expanding for the results in [6, 10]. Based on the BO-B-MKdV equation, the conservation laws associated with the equation and dissipation effect are discussed and some conserved quantities of Rossby solitary waves are obtained
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