https://doi.org/10.1140/epjp/s13360-021-01327-w
Regular Article
Solitary wave solitons to one model in the shallow water waves
1
Department of Mathematics, Faculty of Education, Erciyes University, 38039, Melikgazi-Kayseri, Turkey
2
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
3
Department of Mathematics and Science Education, Faculty of Education, Harran University, Sanliurfa, Turkey
Received:
7
January
2021
Accepted:
15
March
2021
Published online:
24
March
2021
The current study utilizes the generalized 
-expansion method, the generalized 
-
method and He’s semi-inverse variational method in constructing various soliton and other solutions to the (2+1)-dimensional coupled variant Boussinesq equations which describes the elevation of water wave surface for slowly modulated shallow water waves in lakes and ocean beaches. The system represents collision of a nonlinear wave propagating along y-axis and long wave along x-axis. The integration mechanism that was adopted is modified direct algebraic method, which extracts different solitons (dark and singular) and combo (dark-singular) solitons for different values of parameters. The existence criteria for solitons production is also established for both Kerr and power nonlinearities. Additionally, some other solutions known as singular periodic and rational are also emerged in the process of derivation
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
