Considerable traveling wave solutions of a generalized Hietarinta-type equation

• Published in: International Journal of Mathematics and Computer in Engineering 2024-09
• Main Author: Mahmud, Adnan Ahmad
• Format: Article
• Language: English
• ISSN: 2956-7068; 2956-7068
• DOI: 10.2478/ijmce-2025-0015

This work effectively utilizes the modified extended tanh− function approach 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 has been 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 have been shown using two- and three-dimensional graphics and suitable arbitrary parameters to demonstrate their physical and dynamic results. Two-dimensional graphs have 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 have also been figured out with the help of the operation that gives values to the free parameters.