Abstract: This paper investigates the number of solitary periodic wave solutions for a class of perturbed generalized KdV (pgKdV) equations with two arbitrarily high‑order nonlinear terms. By applying the traveling wave transformation, the original partial differential equation is reduced to a planar ordinary differential system. Using geometric singular perturbation theory, the existence and counting of solitary periodic wave solutions are transformed into the problem of zero distribution of an Abel integral. For this Abel integral, the Chebyshev system criterion is employed to prove that any linear combination of its generating elements has at most one zero in the energy interval. Consequently, the original system admits at most one solitary periodic wave solution.

Key words:  , KdV equation, Abel integral, Chebyshev property, Solitary periodic wave solution, Descartes' rule of signs