This paper systematically studies the qualitative properties of solutions and the construction of quasiperiodic solutions for the non-homogeneous KdV-mKdV equations with unbounded boundary conditions. Based on prior estimation theory and the definition of uniform fractional derivatives, continuous dependence and boundedness estimates for the solutions of the equations are established. By transforming the equations into ordinary differential equations via a traveling wave transformation, the waveform stability of the traveling wave solutions is revealed. Numerical simulation methods are used to verify the long-term conservation of soliton solutions, and the homogeneous equilibrium method and Maple calculations are employed to construct the analytical form of quasiperiodic solutions. The results indicate that under unbounded non-homogeneous conditions, the behavior of the solutions to Equation \( u_t + 2\alpha uu_x – 3\beta u^2u_x + \varepsilon u_{xxx} = 0 \) is significantly influenced by the sign of the nonlinear term and the parameter matching relationship, and the quasi-periodic solutions exhibit rich dynamical characteristics ranging from localized freak waves to asymptotically periodic waves.
