Chaplygin's equation

The Chaplygin 's equation, named after the Russian-Soviet aerodynamics Sergei Alexeyevich Chaplygin, is an exactly linearized potential equation of a stationary planar gas flow. The equation is given in polar coordinates of the hodograph plane. The flow is isentropic case without shock waves.

Using the Legendre transformation yields the Chaplygin equation:

Where Φ the conjugated potential, δ is the angle between velocity direction and x-axis, v is the magnitude of the velocity and c is the local speed of sound. The solution of non-linear potential equation is the solution of a linear equation of the function Φ (c, δ ) has been returned, but not in the boundary conditions are linear.