Abstract
The (2+1)-dimensional generalized Benjamin-Ono equation models the propagation of small-amplitude, long-wavelength waves on the surface of shallow water. Constructing explicit solutions of the (2+1)-dimensional generalized Benjamin-Ono equation not only provides theoretical support for experimental investigations but also offers a rigorous basis for addressing applied problems arising in nonlinear wave dynamics. In this work, we investigate wave propagation governed by the (2+1)-dimensional generalized Benjamin-Ono equation in nonlinear media, accounting for dispersive effects. To this end, the sine-cosine function method and the hyperbolic tangent method are employed as analytical tools for deriving explicit solutions. The methods prove effective for a broad class of nonlinear equations encountered in mathematical physics. Using these approaches, periodic-wave solutions and solitary wave solutions are obtained, and to illustrate the obtained results, we plot 3D and 2D plots by setting suitable values of the involved parameters.