The Traveling Wave Solutions and Their Bifurcations for the BBM-Like B(m,n) Equations
We investigate the traveling wave solutions and their bifurcations for the BBM-like B(m,n) equations ut+αux+β(um)x−γ(un)xxt=0 by using bifurcation method and numerical simulation approach of dynamical systems. Firstly, for BBM-like B(3,2) equation, we obtain some precise expressions of traveling wav...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/490341 |
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| Summary: | We investigate the traveling wave solutions and their bifurcations for the BBM-like B(m,n) equations ut+αux+β(um)x−γ(un)xxt=0 by using bifurcation method and numerical simulation approach of dynamical systems. Firstly, for BBM-like B(3,2) equation, we obtain some precise expressions of traveling wave solutions, which include periodic blow-up and periodic wave solution, peakon and periodic peakon wave solution, and solitary wave and blow-up solution. Furthermore, we reveal the relationships among these solutions theoretically. Secondly, for BBM-like B(4,2) equation, we construct two periodic wave solutions and two blow-up solutions. In order to confirm the correctness of these solutions, we also check them by software Mathematica. |
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| ISSN: | 1110-757X 1687-0042 |