Traveling wave solutions for fifth-order KdV type equations with time-dependent coefficients

We investigate two families of fifth-order KdV equations with time-dependent coefficients and linear damping term. These models apply to the description of envelope wave dynamics in inhomogeneous systems modeled by KdV-type equation. The modified sine-cosine method is used to construct exact periodic solutions and solitons solutions for the wave equations. The conditions of existence and uniqueness of exact solutions are also presented. The obtained results show that the sine-cosine.method provides a powerful mathematical tool for solving nonlinear equations with variable coefficients.