Lump, lump-stripe, and breather wave solutions to the (2 + 1)-dimensional Sawada-Kotera equation in fluid mechanics

Md Emran Ali; Farjana Bilkis; Gour Chandra Paul; Dipankar Kumar; Hasibun Naher

doi:10.1016/j.heliyon.2021.e07966

Lump, lump-stripe, and breather wave solutions to the (2 + 1)-dimensional Sawada-Kotera equation in fluid mechanics

Heliyon. 2021 Sep 21;7(9):e07966. doi: 10.1016/j.heliyon.2021.e07966. eCollection 2021 Sep.

Authors

Md Emran Ali^{1

2}, Farjana Bilkis³, Gour Chandra Paul², Dipankar Kumar⁴, Hasibun Naher⁵

Affiliations

¹ Department of Textile Engineering, Northern University Bangladesh, Dhaka 1230, Bangladesh.
² Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh.
³ Department of Science and Humanities, Bangladesh Army International University of Science and Technology, Cumilla 3501, Bangladesh.
⁴ Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj 8100, Bangladesh.
⁵ Department of Mathematics and Natural Sciences, BRAC University, 66 Mohakhali, Dhaka 1212, Bangladesh.

Abstract

The present study investigates the lump, one-stripe, lump-stripe, and breather wave solutions to the (2+1)-dimensional Sawada-Kotera equation using the Hirota bilinear method. For lump and lump-stripe solutions, a quadratic polynomial function, and a quadratic polynomial function in conjunction with an exponential term are assumed for the unknown function f giving the solution to the mentioned equation, respectively. On the other hand, only an exponential function is considered for one-stripe solutions. Besides, the homoclinic test approach is adopted for constructing breather wave solutions. The propagations of the attained lump, lump-stripe, and breather wave solutions are shown through some graphical illustrations. The graphical outputs demonstrate that the lump wave moves along the straight line $y = - x$ and exponentially decreases away from the origin of the spatial domain. On the other hand, lump-kink solutions illustrate the fission and fusion interaction behaviors upon the selection of the free parameters. Fission and fusion processes show that the stripe soliton splits into a stripe soliton and a lump soliton, and then the lump soliton merges into one stripe soliton. In addition, the achieved breather waves illustrate the periodic behaviors in the xy-plane. The outcomes of the study can be useful for a better understanding of the physical nature of long waves in shallow water under gravity.

Keywords: ( 2 + 1 ) -dimensional Sawada-Kotera equation; Breather wave solutions; Hirota bilinear method; Homoclinic test approach; Lump solutions; Lump-stripe solutions.