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| Travelling Wave Solutions and Conservation Laws of the (2+1)-dimensional Broer-Kaup-Kupershmidt Equatio |
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| KeyWord:The (2+1)-dimensional Broer-Kaup-Kupershmidt equation Travelling wave solutions Conservation laws Multiplier method |
| Author Name | Affiliation | | Lijun Zhang | College of Mathematics and Systems Science,
Shandong University of Science and Technology, Qingdao, Shandong 266590, China | | Innocent Simbanefayi | International Institute for Symmetry Analysis and
Mathematical Modelling, Department of Mathematical Sciences,
North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa | | Chaudry Masood Khalique | International Institute for Symmetry Analysis and
Mathematical Modelling, Department of Mathematical Sciences,
North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa |
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| Abstract: |
| The travelling wave solutions and conservation laws of the (2+1)-dimensional Broer-Kaup-Kupershmidt (BKK) equation are considered in this paper. Under the travelling wave frame, the BKK equation is transformed to a system of ordinary differential equations (ODEs) with two dependent variables. Therefore, it happens that one dependent variable $u$ can be decoupled into a second order ODE that corresponds to a Hamiltonian planar dynamical system involving three arbitrary constants. By using the bifurcation analysis, we obtain the bounded travelling wave solutions $u$, which include the kink, anti-kink and periodic wave solutions. Finally, the conservation laws of the BBK equation are derived by employing the multiplier approach. |
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