Burgers' equation
![](/Images/godic/202501/02/Inviscid_Burgers_Equation_in_Two_Dimensions3105.gif")
![This is a numerical solution of the viscous two dimensional Burgers equation using an initial Gaussian profile. We see shock formation, and dissipation of the shock due to viscosity as it travels.](/Images/godic/202501/02/Solution_of_the_viscous_two_dimensional_Burgers_equation3105.gif")
Burgers' equation is a fundamental partial differential equation occurring in various areas of applied mathematics, such as fluid mechanics, nonlinear acoustics, gas dynamics, traffic flow. It is named for Johannes Martinus Burgers (1895–1981).
For a given field ![y(x,t)](/Images/godic/202501/02/0486ae10e0e493b2faa88fb207d7d8c93105.png")
and diffusion coefficient (or viscosity, as in the original fluid mechanical context) ![d](/Images/godic/202501/02/8277e0910d750195b448797616e091ad3105.png")
, the general form of Burgers' equation (also known as viscous Burgers' equation) in one space dimension is the dissipative system: