A Comparative Study of Exact Solutions for the Two Nonlinear Partial Differential Equations Using the (G'⁄G)-Expansion Method

Abstract

In the present work, the -expansion technique is applied to construct closed-form traveling-wave solutions for two nonlinear systems: the modified dispersive water-wave (MDWW) system and the variant Boussinesq system. Compared with more elaborate symbolic approaches, this technique reaches explicit, verifiable solution families with comparatively little algebraic overhead, which in turn sheds light on how these nonlinear systems behave. Because it converts an otherwise unwieldy governing equation into a tractable algebraic system, the method is well suited to producing accurate closed-form expressions. The results reported here support the view that the -expansion approach is a useful tool both for the theoretical study of nonlinear wave phenomena and for problems arising in applied nonlinear dynamics.