On deviations from linear wave motion in inhomogeneous stars
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.