Abstract
In this work, a method called the [Formula: see text]-extension method which is effective and yields soliton solutions is utilized to scrutinize the nonlinear Burger-like equation with beta derivative and the nonlinear Boussinesq–Burger equation with beta derivative. The method is applied in a reliable and efficient style using a symbolic computing program called Maple. In addition, some graphs of the solutions are presented. When these equations are solved using the suggested method, several novel exact solutions have been achieved that differ from those found by utilizing them earlier. The findings of this work add to the body of literature by offering insightful definitions of different nonlinear systems. The outcomes showed that the proposed technique is a useful mathematical tool and the symbolic computation program makes them easier, more reliable and faster.
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