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Modified (1+1)-Dimensional Displacement Shallow Water Wave System |
| LIU Ping1, YANG Jian-Jun1, REN Bo2 |
1College of Electron and Information Engineering, University of Electronic Science and Technology of China Zhongshan Institute, Zhongshan 528402
2Institute of Nonlinear Science, Shaoxing University, Shaoxing 312000
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| Cite this article: |
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LIU Ping, YANG Jian-Jun, REN Bo 2013 Chin. Phys. Lett. 30 100201 |
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Abstract Recently, a (1+1)-dimensional displacement shallow water wave system (1DDSWWS) was constructed by applying variational principle of the analytic mechanics under the Lagrange coordinates. However, fluid viscidity is not considered in the 1DDSWWS, which is the same as the famous Korteweg-de Vries (KdV) equation. We modify the 1DDSWWS and add the term related to fluid viscosity to the model by means of dimension analysis. For the perfect fluids, the coefficient of kinematic viscosity is zero, then the modified 1DDSWWS (M1DDSWWS) will degenerate to 1DDSWWS. The KdV-Burgers equation and the Abel equation can be derived from the M1DDSWWS. The calculation on symmetry shows that the system is invariant under the Galilean transformations and the spacetime translations. Two types of exact solutions and some evolution graphs of the M1DDSWWS are proposed.
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Received: 03 May 2013
Published: 21 November 2013
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| PACS: |
02.30.Jr
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(Partial differential equations)
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47.10.-g
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(General theory in fluid dynamics)
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02.30.Ik
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(Integrable systems)
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