Euler–Poisson–Darboux equation

In mathematics, the Euler–Poisson–Darboux equation is the partial differential equation


 * $$u_{x,y}+\frac{N(u_x+u_y)}{x+y}=0. $$

This equation is named for Siméon Poisson, Leonhard Euler, and Gaston Darboux. It plays an important role in solving the classical wave equation.

This equation is related to


 * $$u_{rr}+\frac{m}{r}u_r-u_{tt}=0, $$

by $$ x=r+t $$, $$ y=r-t $$, where $$ N=\frac{m}{2} $$ and some sources quote this equation when referring to the Euler–Poisson–Darboux equation.