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Modified generalized Vakhnenko equation; cusped solitons; loop solitons; periodic cusp wave solutions; smooth periodic wave solutions; pseudopeakon solitons; smooth soliton solutions.

By using the bifurcation theory of planar dynamical systems and the qualitative theory of differential equations, we studied the dynamical behaviours and exact travelling wave solutions of the modified generalized Vakhnenko equation (mGVE). As a result, we obtained all possible bifurcation parametric sets and many explicit formulas of smooth and non-smooth travelling waves such as cusped solitons, loop solitons, periodic cusp waves, pseudopeakon solitons, smooth periodic waves and smooth solitons. Moreover, we provided some numerical simulations of these solutions.

JUNJUN XIAO¹ DAHE FENG ^{1 2} XIA MENG¹ YUANQUAN CHENG¹

1. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi 541004, People’s Republic of China
2. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, Guizhou 550025, People’s Republic of China

Published

16 January 2017

Manuscript received

12 May 2015

Manuscript revised

24 May 2016

Accepted

17 June 2016

Early published

13 December 2016