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Symmetry reduction and exact solutions of the (3+1)-dimensional Zakharovben–Kuznetsov equation |
| Dong Zhong-Zhou(董仲周)a), Chen Yong(陈勇)a)†, and Lang Yan-Huai(郎艳怀)b) |
| a Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China; b Department of Mathematics, Shanghai University of Finance and Economics, Shanghai 200434, China |
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Abstract By means of the classical method, we investigate the (3+1)-dimensional Zakharov–Kuznetsov equation. The symmetry group of the (3+1)-dimensional Zakharov–Kuznetsov equation is studied first and the theorem of group invariant solutions is constructed. Then using the associated vector fields of the obtained symmetry, we give the one-, two-, and three-parameter optimal systems of group-invariant solutions. Based on the optimal system, we derive the reductions and some new solutions of the (3+1)-dimensional Zakharov–Kuznetsov equation.
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Received: 30 November 2009
Revised: 29 January 2010
Accepted manuscript online:
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10735030 and 90718041), Shanghai Leading Academic Discipline Project, China (Grant No. B412), Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT0734). |
Cite this article:
Dong Zhong-Zhou(董仲周), Chen Yong(陈勇), and Lang Yan-Huai(郎艳怀) Symmetry reduction and exact solutions of the (3+1)-dimensional Zakharovben–Kuznetsov equation 2010 Chin. Phys. B 19 090205
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