| Volume 7, Number 4, 2017, Pages 1417-1430 DOI：10.11948/2017086 |
| Sub-manifold and traveling wave solutions of Ito''s 5th-order mKdV equation |
| Lijun Zhang,Haixia Chang,Chaudry Masood Khalique |
| Keywords:Ito''s 5th-order mKdV equation, traveling wave solutions, subequations, planar dynamical systems. |
| Abstract: |
| In this paper, we study Ito''s 5th-order mKdV equation with the aid of symbolic computation system and by qualitative analysis of planar dynamical systems. We show that the corresponding higher-order ordinary differential equation of Ito''s 5th-order mKdV equation, for some particular values of the parameter, possesses some sub-manifolds defined by planar dynamical systems. Some solitary wave solutions, kink and periodic wave solutions of the Ito''s 5th-order mKdV equation for these particular values of the parameter are obtained by studying the bifurcation and solutions of the corresponding planar dynamical systems. |
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