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

Chunlei Wang,Xiaoen Zhang,Baoshu Yin,Yong Zhang

doi:10.1155/2015/126508

Abstract

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.

Highlights

In soliton theory, it is an important task to find new integrable hierarchies and their coupling systems
The results showed that the amplitude of Rossby solitary waves which propagate in a line satisfies the (1 + 1)-dimensional mKdV equation
The (2 + 1)-dimensional mKdV hierarchy has been obtained in this paper, we note that it is difficult to obtain all the (2 + 1)-dimensional hierarchies by using the generalized Tu scheme and not every (2 + 1)-dimensional hierarchy has its own Hamiltonian structure

Summary

Introduction

It is an important task to find new integrable hierarchies and their coupling systems. We obtain some solutions of the (2 + 1)dimensional mKdV equation based on the classical Riccati equation. By employing these solutions, similar to fiber soliton communication, we will study the chirp effect of Rossby solitary waves. The results showed that the amplitude of Rossby solitary waves which propagate in a line satisfies the (1 + 1)-dimensional mKdV equation. In this paper, we use the same way to describe the chirp effect of the Rossby solitary waves based on the (2 + 1)-dimensional mKdV equation.

The Chirp Effect of Rossby Solitary Waves

Conclusions