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International Journal of Differential Equations
Volume 2016 (2016), Article ID 1846341, 7 pages
Research Article

Exact Solutions Superimposed with Nonlinear Plane Waves

1Department of Mathematics, University of Mumbai, Mumbai 400 098, India
2Department of Mathematics, North Maharashtra University, Jalgaon 425 001, India

Received 9 February 2016; Accepted 20 April 2016

Academic Editor: Wen-Xiu Ma

Copyright © 2016 B. S. Desale and Vivek Sharma. 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.


The flow of fluid in atmosphere and ocean is governed by rotating stratified Boussinesq equations. Through the literature, we found that many researchers are trying to find the solutions of rotating stratified Boussinesq equations. In this paper, we have obtained special exact solutions and nonlinear plane waves. Finally, we provide exact solutions to rotating stratified Boussinesq equations with large scale motion superimposed with the nonlinear plane waves. In support of our investigations, we provided two examples: one described the special exact solution and in second example, we have determined the special exact solution superimposed with nonlinear plane wave. Also, we depicted some integral curves that represent the flow of an incompressible fluid particle on the plane as the particular case.