EXACT SOLITARY WAVE AND PERIODIC WAVE SOLUTIONS OF THE KAUP-KUPERSCHMIDT EQUATION

Lijun Zhang; C. M. Khalique

doi:10.11948/2015039

2015 Volume 5 Issue 3

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Lijun Zhang, C. M. Khalique. EXACT SOLITARY WAVE AND PERIODIC WAVE SOLUTIONS OF THE KAUP-KUPERSCHMIDT EQUATION[J]. Journal of Applied Analysis & Computation, 2015, 5(3): 485-495. doi: 10.11948/2015039

Citation:

Lijun Zhang, C. M. Khalique. EXACT SOLITARY WAVE AND PERIODIC WAVE SOLUTIONS OF THE KAUP-KUPERSCHMIDT EQUATION[J]. Journal of Applied Analysis & Computation, 2015, 5(3): 485-495. doi: 10.11948/2015039

EXACT SOLITARY WAVE AND PERIODIC WAVE SOLUTIONS OF THE KAUP-KUPERSCHMIDT EQUATION

1 Department of Mathematics, Zhejiang Sci-Tech University, Xiasha, 310018, Hangzhou, China;
2 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

Abstract

In this paper we investigate the exact traveling wave solutions of the fifth-order Kaup-Kuperschmidt equation. The bifurcation and exact solutions of a general first-order nonlinear equation are investigated firstly. With the help of Maple and by using the bifurcation and exact solutions of two derived subequations, we obtain two families of solitary wave solutions and two families of periodic wave solutions of the KK equation. The relationship of the two subequations and the two known first integrals are analyzed.
- Traveling wave solutions /
- the Kaup-Kuperschmidt equation /
- dynamical system method /
- Jacobi elliptic function /
- subequation
MSC: 35Q51;35Q53;34C23;34C37

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