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Chin. Phys. B, 2013, Vol. 22(5): 050204    DOI: 10.1088/1674-1056/22/5/050204
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Exact solutions of (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations

Liu Pinga, Li Zi-Liangb
a College of Electron and Information Engineering, University of Electronic Scienceand Technology of China Zhongshan Institute, Zhongshan 528402, China;
b Physical Oceanography Laboratory, College of Physical and Environment Oceanography, Ocean University of China, Qingdao 266100, China
Abstract  The symmetries and the exact solutions of the (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations, which describe the atmospheric gravity waves, are studied in this paper. The calculation on symmetry shows that the equations are invariant under the Galilean transformations, the scaling transformations, and the space-time translations. Three types of symmetry reduction equations and similar solutions for the (3+1)-dimensional INHB equations are proposed. Traveling and non-traveling wave solutions of the INHB equations are demonstrated. The evolutions of the wind velocities in latitudinal, longitudinal, and vertical directions with space-time are demonstrated. The periodicity and the atmosphere viscosity are displayed in the (3+1)-dimensional INHB system.
Keywords:  (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations      atmospheric gravity waves      symmetries      exact solutions  
Received:  25 August 2012      Revised:  15 November 2012      Accepted manuscript online: 
PACS:  02.30.Jr (Partial differential equations)  
  02.20.Hj (Classical groups)  
  02.20.Sv (Lie algebras of Lie groups)  
  92.60.hh (Acoustic gravity waves, tides, and compressional waves)  
Fund: Projet supported by the Natural Science Foundation of Guangdong Province, China (Grant Nos. 10452840301004616 and S2011040000403), the National Natural Science Foundation of China (Grant No. 41176005), and the Science and Technology Project Foundation of Zhongshan, China (Grnat No. 20123A326).
Corresponding Authors:  Li Zi-Liang     E-mail:

Cite this article: 

Liu Ping, Li Zi-Liang Exact solutions of (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations 2013 Chin. Phys. B 22 050204

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