Abstract
Linear waves considered in Chap. 2 describe perturbations with small amplitudes. In the astrophysical conditions, however, a strong energy release gives often rise to large-amplitude perturbations, which cannot be fully accommodated by the linear theory and so require non-linear treatment. In this chapter we consider a number of important examples of the nonlinear waves—simple waves, solitons, and discontinuities—with the use of exact or approximate analytical methods.
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- 1.
This is derived as follows:
$$Tc_{V }^{-1}=(\partial _{s}T)_{ V =1/\rho }=(\partial _{s}T)_{\rho }=\frac{\partial (s,p)} {\partial (s,\rho )} \frac{\partial (T,\rho )} {\partial (s,p)} =(\partial _{\rho }p)_{s}[(\partial _{s}T)_{p}(\partial _{p}\rho )_{s}-(\partial _{p}T)_{s}(\partial _{s}\rho )_{p}] =Tc_{P}^{-1}-(\partial _{\rho }p)_{s}(\partial _{p}T)_{s}(\partial _{s}\rho )_{p}.$$ - 2.
The structure of shock waves in a dense high-temperature plasma was studied by Imshennik and Bobrova (1997).
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Fleishman, G.D., Toptygin, I.N. (2013). Nonlinear MHD Waves and Discontinuities. In: Cosmic Electrodynamics. Astrophysics and Space Science Library, vol 388. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5782-4_5
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