Ali Md Emran, Bilkis Farjana, Paul Gour Chandra, Kumar Dipankar, Naher Hasibun
Department of Textile Engineering, Northern University Bangladesh, Dhaka 1230, Bangladesh.
Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh.
Heliyon. 2021 Sep 21;7(9):e07966. doi: 10.1016/j.heliyon.2021.e07966. eCollection 2021 Sep.
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 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 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 -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.
本研究使用广田双线性方法研究了(2 + 1)维泽田-小寺方程的块状、单条纹、块状-条纹和呼吸波解。对于块状和块状-条纹解，分别假设未知函数为二次多项式函数以及二次多项式函数与指数项的结合，从而得到上述方程的解。另一方面，对于单条纹解，仅考虑指数函数。此外，采用同宿测试方法来构造呼吸波解。通过一些图形展示了所得到的块状、块状-条纹和呼吸波解的传播情况。图形输出表明，块状波沿直线移动，并在远离空间域原点时呈指数衰减。另一方面，块状扭结解在自由参数的选择上展现出裂变和融合相互作用行为。裂变和融合过程表明，条纹孤子分裂为一个条纹孤子和一个块状孤子，然后块状孤子合并为一个条纹孤子。此外，所得到的呼吸波在(x - t)平面上呈现出周期性行为。该研究结果有助于更好地理解重力作用下浅水中长波的物理性质。
