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Mathematical Problems in Engineering
Volume 2018, Article ID 4276591, 12 pages
https://doi.org/10.1155/2018/4276591
Research Article

Three-Dimensional Coupled NLS Equations for Envelope Gravity Solitary Waves in Baroclinic Atmosphere and Modulational Instability

1College of Oceanography, Hohai University, Nanjing 210098, China
2College of Roads and Bridges, Nanjing Vocational Institute of Transport Technology, Nanjing 211188, China
3College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, China
4Key Laboratory of Meteorological Disaster of Ministry of Education, Nanjing University of Information Science and Technology, Nanjing 210044, China

Correspondence should be addressed to Ruyun Wang; nc.ude.uhh@yrgnaw

Received 3 August 2017; Accepted 30 October 2017; Published 8 January 2018

Academic Editor: Qin Yuming

Copyright © 2018 Baojun Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Envelope gravity solitary waves are an important research hot spot in the field of solitary wave. And the weakly nonlinear model equations system is a part of the research of envelope gravity solitary waves. Because of the lack of technology and theory, previous studies tried hard to reduce the variable numbers and constructed the two-dimensional model in barotropic atmosphere and could only describe the propagation feature in a direction. But for the propagation of envelope gravity solitary waves in real ocean ridges and atmospheric mountains, the three-dimensional model is more appropriate. Meanwhile, the baroclinic problem of atmosphere is also an inevitable topic. In the paper, the three-dimensional coupled nonlinear Schrödinger (CNLS) equations are presented to describe the evolution of envelope gravity solitary waves in baroclinic atmosphere, which are derived from the basic dynamic equations by employing perturbation and multiscale methods. The model overcomes two disadvantages: (1) baroclinic problem and (2) propagation path problem. Then, based on trial function method, we deduce the solution of the CNLS equations. Finally, modulational instability of wave trains is also discussed.