Generative Artificial Intelligence (AI) is reshaping digital marketing by creating automated content, personalizing campaigns, and offering new ways to engage consumers. This systematic review examines research on generative AI, highlighting both its technological progress and the ethical, technical, and organizational hurdles that could limit its use. We used a PRISMA-based method to search major databases (ACM Digital Library, IEEE Xplore, and Scopus) for peer-reviewed studies published from 2018 to 2025. Our findings reveal major gains in text creation, image generation, and multimodal campaigns, which can lower costs and spark creative thinking. Still, data privacy, bias in models, and laws around compliance show the need for clear and responsible adoption. By bringing in ideas from Innovation Diffusion Theory and the Technology Acceptance Model, this review shows how organizational culture and perceived value interact with ethical frameworks to shape how generative AI tools take hold. We provide insights for marketers who want to apply generative AI in a responsible way and set a path for future research aimed at protecting consumer trust.

This study offers an in-depth exploration of traveling wave solutions to the simplified modified Camassa-Holm (SMCH) equation through the application of the modified S-expansion method. Utilizing a traveling wave transformation, the SMCH equation is converted into a nonlinear ordinary differential equation, from which a wide range of exact solutions is systematically obtained. The modified S-expansion method, implemented using the Maple software, proves to be a robust and efficient analytical tool, yielding a variety of soliton solutions such as kink, bright, and dark solitons. To capture the intricate behavior of these solutions, MATLAB is employed to produce detailed 2D, 3D, and contour visualizations that reveal their structural features and propagation dynamics. A comparative assessment with the modified simple equation method and the exp(-ϕ(η))-expansion method highlights the modified S-expansion method's superior accuracy, simplicity, and adaptability to solve nonlinear partial differential equations. Significantly, the method also extends to fractional-order equations, showcasing its broad applicability in nonlinear system analysis. Key solutions are graphically represented under constrained parameter values to emphasize the core propagation features. Overall, this work enhances the current analytical methods to solve both classical and fractional-order nonlinear partial differential equations (PDEs) and offers a valuable foundation for future research into closed-form traveling wave solutions across various disciplines.