... using a new kind of operator, the Yang-Abdel-Aty-Cattani (YAC) operator. That is a new concept. The revised model is solved using a well-known semi-analytic technique, the homotopy perturbation method (HPM), with the help of the Laplace transform. Also, the obtained solutions are compared with the exact...

.... Homotopy perturbation method Water surface elevation Basin depth Interval shallow water wave equations η ∼ ( x , 0 ) = [ η ¯ ,   η ¯ ]     e − ( x − 20 ) 2 8 M ∼ ( x , 0 ) = [ M ¯ ,   M ¯ ]     e − ( x − 20 ) 2...

... are transformed into dimensionless nonlinear ordinary differential equations by similarity transformation. Analytical technique, namely the homotopy perturbation method (HPM) combining with Padé approximants and finite difference method, are used to solve dimensionless non‐linear ordinary differential equations...