CLOSED FORM EXACT SOLUTIONS TO THE COMBINED KDV-MKDV EQUATION AND THE (2+1)-DIMENSIONAL GBS EQUATION VIA THE RICCATI SUB-EQUATION METHOD

บทคัดย่อ

The main goal of the present study is to find exact traveling wave solutions of the combined kdv-mkdv equation and the (2+1)-dimensional generalized breaking soliton equation using the Riccati sub-equation method. The obtained solutions are shown by hyperbolic and trigonometric functions, which can be transformed into kink waves and periodic waves. Their graphical representations are two-dimensional, three-dimensional graphs, and contour graphs are shown using suitable parameter values. Additionally, the results proved that the method employed in this study is a powerful analytical tool for obtaining exact traveling wave solutions to nonlinear models that are used in many different engineering and scientific disciplines.