(5) Multi-soliton fusion phenomenon of Burgers equation and fission, fusion phenomenon of Sharma–Tasso–Olver equation

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Harun Or-Roshid ^{a , ∗} , M.M. Rashidi ^{b , c}
a Department of Mathematics, Pabna University of Science and Technology, Pabna 6600, Bangladesh

b Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University, 4800 Cao An Rd., Jiading, Shanghai 201804, China

c ENN-Tongji Clean Energy Institute of Advanced Studies, China

Received 18 February 2017; received in revised form 11 April 2017; accepted 18 April 2017
Available online 19 May 2017

Abstract
A direct rational exponential scheme is proposed to construct exact multi-soliton solutions and its fission, fusion phenomena after interaction of the solitons has been discussed. We have considered the Burgers and Sharma–Tasso–Olver equation as two concrete examples to show the fission and fusion of the solitary wave and the solitons, respectively. We improve different structured multi-soliton solutions with possible conditions for fission and fusion of the Burgers and the Sharma–Tasso–Olver equations arises in plasma physics and in ocean dynamics. The amplitude and velocity relations between solitons and/or solitary waves before and after interactions are given and a possible condition for fission and fusion is proposed. Furthermore, three-dimensional plots of the wave solutions are given to visualize the dynamics of the model.
© 2017 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license. ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

Keywords: Direct rational exponential scheme; Burger equation; Sharma–Tasso–Olver equation; Traveling wave solutions; Multi-soliton.

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