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The hydrodynamic equations for the large-amplitude, adiabatic pulsations of a spherically symmetric, inhomogeneous star are solved by a method of approximation in which the form of the fluid velocity is specified a priori. The assumed velocity is a nonlinear function of the radius and contains two arbitrary functions of time. These two functions are determined by a pair of second-order, quasi-linear, ordinary differential equations, and an analytic, periodic solution to these equations is constructed. This solution corresponds to large amplitude, anharmonic, nonlinear pulsations of a star in which the fluid velocity is a travelling wave. A specific inhomogeneous star is studied to demonstrate the feasibility of numerically solving the pair of differential equations and of constructing the periodic solution.

On deviations from linear wave motion in inhomogeneous stars