![Sample our Bioscience journals, sign in here to start your access, Latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5925/TOC-Subject-Sample-2021-Bioscience.jpg"})
Abstract
In this study, lump and two classes of interaction, multi-stripe, and breather wave solutions for the (3+1)-dimensional generalized shallow water equation are presented via the Hirota bilinear method. Interaction solutions are found between one-lump and one-stripe, and one-lump and two-stripes solutions by combining a quadratic function and an exponential function, and a quadratic function and a hyperbolic cosine or double exponential functions, respectively. Dynamical behaviours of some obtained valid solutions are presented through some graphs. The physical interpretation of fission-fusion dynamics is also explained graphically through lump-kink interaction solutions. During the fission-fusion interaction process, it is seen that stripe solitons split into a stripe and a lump soliton, and then the lump and stripe solitons fuse together. During this process, a rogue wave is found between one lump and twin stripes soliton at Furthermore, multi-stripe and breather wave solutions are investigated by choosing the appropriate functions and the values for the free parameters. The multi-stripe waves are found to be nonsingular and rectangular hyperbolic shaped. On the other hand, breather waves are found to be periodic, which can evolve periodically along a straight line in the xy-plane. The produced wave solutions might be helpful to understand the propagation behaviour of waves in shallow water.
Acknowledgments
We would like to thank the editor and two anonymous referees for their insightful comments and helpful suggestions that helped us to improve this manuscript.
Disclosure statement
No potential conflict of interest was reported by the author(s).