ZK-Burgers equation for three-dimensional Rossby solitary waves and its solutions as well as chirp effect

Advances in Difference Equations

Hong Wei Yang¹  De Zhou Yang²  Bao Shu Yin²  Xing Ru Feng³  Huan He Dong³  Zhen Hua Xu³ 

[1] College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao, China;Function Laboratory for Ocean Dynamics and Climate, Qingdao National Laboratory for Marine Science and Technology, Qingdao, China;Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Chinese Academy of Sciences, Qingdao, China

关键词: three-dimensional Rossby solitary waves;    ZK-Burgers equation;    Hirota method;    ration solution;    chirp effect;    02.30.Jr;    43.75.Fg;    92.10.Hm;   

DOI  :  10.1186/s13662-016-0901-8

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Two-dimensional Rossby solitary waves propagating in a line have attracted much attention in the past decade, whereas there is few research on three-dimensional Rossby solitary waves. But as is well known, three-dimensional Rossby solitary waves are more suitable for real ocean and atmosphere conditions. In this paper, using multiscale and perturbation expansion method, a new Zakharov-Kuznetsov (ZK)-Burgers equation is derived to describe three-dimensional Rossby solitary waves that propagate in a plane. By analyzing the equation we obtain the conservation laws of three-dimensional Rossby solitary waves. Based on the sine-cosine method, we give the classical solitary wave solutions of the ZK equation; on the other hand, by the Hirota method we also obtain the rational solutions, which are similar to the solutions of the Benjamin-Ono (BO) equation, the solutions of which can describe the algebraic solitary waves. The rational solutions of the ZK equations are worth of attention. Finally, with the help of the classical solitary wave solutions, similar to the fiber soliton communication, we discuss the dissipation and chirp effect of three-dimensional Rossby solitary waves.

【 授权许可】

CC BY