Chaplygin's equation

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In mathematics, Chaplygin's equation, named after Sergei Alekseevich Chaplygin, is a nonlinear partial differential equation useful in the study of transonic flow. It is

\Psi_{\theta\theta}+ \frac{v^2}{1-\frac{v^2}{c^2}}\Psi_{vv}+v\Psi_v=0.

Here, c = c(v) is the speed of sound, determined by the equation of state of the fluid and Bernoulli's principle.