We use the homotopy analysis method (HAM) to find analytical solutions to the Vakhnenko equation and the Korteweg-de Vries-Burgers (KdV-Burgers) equation, two well-known (2+1)-dimensional nonlinear evolution equations. These solutions are essential for describing complex physical processes in a variety of fields, including nonlinear optics, fluid dynamics, and plasma physics. The convergence of the HAM-based solution is demonstrated using the squared residual error technique. The HAM-based technique shows a strong match with the exact solution to the problems.
