Eur. Phys. J. Plus (2017) 132: 465
https://doi.org/10.1140/epjp/i2017-11747-6

Regular Article

Lump solutions and interaction phenomenon to the third-order nonlinear evolution equation

¹ Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaoundé, Cameroon
² Centre d’Excellence Africain en Technologies de l’Information et de la Communication (CETIC), University of Yaounde I, P.O. Box 812, Yaoundé, Cameroon
³ Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Maroua, P. O. Box 814, Maroua, Cameroon
⁴ Department of Mathematics, California State University-Northridge, 91330-8313, Northridge, CA, USA

^* e-mail: fokostinos@yahoo.fr

Received: 27 August 2017
Accepted: 7 October 2017
Published online: 8 November 2017

Abstract

In this work, the lump solution and the kink solitary wave solution from the (2 + 1) -dimensional third-order evolution equation, using the Hirota bilinear method are obtained through symbolic computation with Maple. We have assumed that the lump solution is centered at the origin, when t = 0 . By considering a mixing positive quadratic function with exponential function, as well as a mixing positive quadratic function with hyperbolic cosine function, interaction solutions like lump-exponential and lump-hyperbolic cosine are presented. A completely non-elastic interaction between a lump and kink soliton is observed, showing that a lump solution can be swallowed by a kink soliton.