Symmetry reduction and exact solutions of the (3+1)-dimensional Zakharovben–Kuznetsov equation

doi:10.1088/1674-1056/19/9/090205

中国物理B ›› 2010, Vol. 19 ›› Issue (9): 90205-090205.doi: 10.1088/1674-1056/19/9/090205

Symmetry reduction and exact solutions of the (3+1)-dimensional Zakharovben–Kuznetsov equation

郎艳怀¹, 董仲周², 陈勇²

(1)Department of Mathematics, Shanghai University of Finance and Economics, Shanghai 200434, China; (2)Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China

收稿日期:2009-11-30 修回日期:2010-01-29 出版日期:2010-09-15 发布日期:2010-09-15
基金资助:
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, Chi

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

Received:2009-11-30 Revised:2010-01-29 Online:2010-09-15 Published:2010-09-15
Supported by:
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).

摘要/Abstract

摘要： 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.

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.

Key words: Zakharov–Kuznetsov equation, classical Lie method, explicit solution

中图分类号:

0290

董仲周, 陈勇, 郎艳怀. Symmetry reduction and exact solutions of the (3+1)-dimensional Zakharovben–Kuznetsov equation[J]. 中国物理B, 2010, 19(9): 90205-090205.

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[J]. Chin. Phys. B, 2010, 19(9): 90205-090205.

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Symmetry reduction and exact solutions of the (3+1)-dimensional Zakharovben–Kuznetsov equation

Symmetry reduction and exact solutions of the (3+1)-dimensional Zakharovben–Kuznetsov equation

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