What kind of system are you examining? Have you looked into how the magnetic field is treated in the solar corona and the solar p-modes? We investigated magnetic fields in white dwarf stars https://ui.adsabs.harvard.edu/#abs/1989ApJ...336..403J/abstract and much literature is devoted to the interaction of nonracial oscillations and magnetic fields in stars.

Thanks, anyway. I am rather interested in spherical wave analyses with and without approximations. The physical model may spherical stars, dust molecular clouds, etc.

The only approximation we make is linear wave theory. The system is very important. Waves inside stars tend to adiabatic because the material is optically thick. Waves in optically thin matter, such as the solar corona, have different characteristics. Waves in interstellar dust clouds aren't spherical when the cloud isn't self-gravitating. Although spherically symmetric waves were the first variable stars to be observed (radial oscillators such as Cepheids, RR Lyrae stars, and Mira stars), nonradial oscillations are far more common throughout the H-R diagram. Nonlinear calculations of Cepheids and RR Lyrae stars are easy to find in the literature (Christy and Cox are among the authors.)

Thanks Dr. Pesnell. Could you please enlist more references on spherical waves?

Thanks Dr. Pesnell. Could you please enlist more references on spherical waves?

J. P. Cox, Theory of Stellar Oscillations, is a good place to start. It's a little old but thorough in theory and observations. Additional references are difficult to provide without knowing your application. Cox is good for stars, but other systems have different approaches.

Thanks. I am interested in the stability of spherical plasma systems, such as spherical molecular clouds, stars, etc. May I get more helps?