Exact Solutions of Atmospheric (2+1)-Dimensional Nonlinear Incompressible Non-hydrostatic Boussinesq Equations |
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| Authors: | Ping Liu Ya-Xiong Wang Bo Ren Jin-Hua Li |
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| Institution: | 1. College of Electron and Information Engineering, University of Electronic Science and Technology of China Zhongshan Institute, Zhongshan 528402, China;
2. School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China;
3. Institute of Nonlinear Science, Shaoxing University, Shaoxing 312000, China;
4. School of Physics and Optoelectronic Engineering, Nanjing University of Information Science and Technology, Nanjing, China |
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| Abstract: | Exact solutions of the atmospheric (2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space. |
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| Keywords: | nonlinear incompressible non-hydrostatic Boussinesq equations exact solutions symmetries function expansion |
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