LAUSR

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