## International Journal of Differential Equations

- Int. J. Differ. Equ.
- Volume 2016 (2016), Article ID 1846341, 7 pages.

### Exact Solutions Superimposed with Nonlinear Plane Waves

#### Abstract

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 ${x}_{\mathrm{1}}+{x}_{\mathrm{2}}=L(\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t})$ as the particular case.

#### Article information

**Source**

Int. J. Differ. Equ., Volume 2016 (2016), Article ID 1846341, 7 pages.

**Dates**

Received: 9 February 2016

Accepted: 20 April 2016

First available in Project Euclid: 21 December 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.ijde/1482352578

**Digital Object Identifier**

doi:10.1155/2016/1846341

**Mathematical Reviews number (MathSciNet)**

MR3510934

**Zentralblatt MATH identifier**

1353.35287

#### Citation

Desale, B. S.; Sharma, Vivek. Exact Solutions Superimposed with Nonlinear Plane Waves. Int. J. Differ. Equ. 2016 (2016), Article ID 1846341, 7 pages. doi:10.1155/2016/1846341. https://projecteuclid.org/euclid.ijde/1482352578