Considerable traveling wave solutions of the generalized Hietarinta-type equation

Abstract This work utilizes the modified extended tanh− function approach effectively in order to scientifically deduce semi-analytic traveling wave solutions for the (2+1)-dimensional fourth-order non-linear generalized Hietarinta-type problem, leading to previously unidentified satisfactory solutions. The proposed model is transformed into a fourth-order non-linear ordinary differential equation via a traveling wave transformation. Some periodic-solitary, original, and oscillating wave solutions to the model under experimentation are acquired in mixed complex trigonometric and logarithmic functions combined with hyperbolic trigonometric functions, and complex rational functions. Assorted solutions are shown using two- and three-dimensional graphics and suitable arbitrary parameters to demonstrate their physical and dynamic results. Two-dimensional graphs are shown how changes in time formally impact the features and structures of the solution. The free parameters (unrestricted parameters) that keep going in the solutions have a big impact on the dynamic behavior of the solutions. Traveling wave, oscillating, periodic, and breather wave solutions are also figured out with the help of the computational operation that gives values to the free parameters.