Novel Exact Traveling Wave Solutions of the (2+1)-Dimensional Calogero-Bogoyavlenskii-Schiff Equation via the Kumar-Malik and Improved F-Expansion Methods

This paper presents a rigorous investigation of analytical solutions for the (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (CBS) equation. To systematically analyze the nonlinear wave structures inherent in the CBS equation, we innovatively employ both the Kumar-Malik method and an improved F-expansion method, successfully constructing multiple families of exact solutions, including hyperbolic functions, trigonometric functions, and rational functions. Using the powerful mapping capabilities of Maple software, the obtained solutions are visualized as 3D plots, 2D graphs, and contour maps; through detailed analysis, kink wave solutions, singular periodic wave solutions, and rational singular solutions are clearly identified. These findings not only significantly expand the solution space for the integer-order CBS equation but also provide fresh theoretical insights into its dynamical characteristics. The results are expected to stimulate new research directions and facilitate substantial progress in nonlinear wave theory.