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Non-local Boussinesq (nlBq) equation; Lie symmetry analysis; extended Kudryashov’s algorithm; multiple exp-function algorithm

In this paper, we study the exact solutions of non-local Boussinesq equation (nlBq) which appears in many scientific fields. We generate dark solitons, singular solitons, a new family of solitons and combo dark–singular soliton-type solutions of nlBq by the extended Kudryashov’s algorithm. Additional solutions such as singular periodic solutions also fall out of this integration scheme. Also, one-soliton, two-soliton and three-soliton type solutions are presented using multiple exp-function algorithm. Lastly, Lie symmetry analysis with the new similarity reductions is also examined.

ABDULLAHI RASHID ADEM¹ YAKUP YILDIRIM² EMRULLAH YASAR²

1. Material Science Innovation and Modelling Focus Area, School of Mathematical and Statistical Sciences, North-West University, Private Bag X 2046, Mmabatho 2735, South Africa
2. Department of Mathematics, Faculty of Arts and Sciences, Uludag University, 16059 Bursa, Turkey

Published

1 February 2019

Manuscript received

28 April 2018

Manuscript revised

9 June 2018

Accepted

12 June 2018

Early published

Unedited version published online

Final version published online

2 January 2019