# Chaplygin's equation

In mathematics, Chaplygin's equation, named after Sergei Alekseevich Chaplygin, is a partial differential equation useful in the study of transonic flow.[1] 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.

## Traveling wave plots

 Chaplygin equation traveling wave plot Chaplygin equation traveling wave plot Chaplygin equation traveling wave plot Chaplygin equation traveling wave plot
 Chaplygin equation traveling wave plot Chaplygin equation traveling wave plot Chaplygin equation traveling wave plot Chaplygin equation traveling wave plot
 Chaplygin equation traveling wave plot Chaplygin equation traveling wave plot

## References

1. ^ Landau, L. D.; Lifshitz, E. M. (1982). Fluid Mechanics (2 ed.). Pergamon Press. p. 432.