Abstract: This paper focuses on the KdV equation to investigate the construction and physical characteristics of its traveling wave solutions. By employing the hyperbolic function method, Wu’s elimination method, and an improved (G^\text'/G) expansion method, the study systematically analyzes the construction process of solutions under different parameter relationships, revealing the regulatory effects of parameters on soliton amplitude, width, and propagation velocity. The results indicate that by imposing algebraic constraints on parameters and (such as geometric progression relations or quadratic constraints), classical elliptic function solutions can be extended into periodic or soliton solutions, enabling a smooth transition between the two. Numerical simulations confirm the stability of soliton solutions and their shape preservation after collisions, while the energy distribution properties of periodic solutions are qualitatively explained through dynamical system bifurcation theory. Additionally, a rational-periodic composite solution is proposed, combining localized attenuation and periodic oscillation characteristics, offering new insights for describing nonlinear waves in dissipative systems. The objective of this study is to systematically analyze the relationships between root parameters to extend the family of traveling wave solutions for the KdV equation, thereby elucidating the influence of parameter modulation on the morphological characteristics of these solutions.