Burgers equation

The Burgers equation is a viscous nonlinear PDE,

u_t+uu_x=\delta u_{xx}, \quad \delta>0

where the dissipative effects are proportional to 𝛿. In the limit of vanishing viscosity, the solution to this equation approaches the shock solution of the Hopf equation if the solution of the latter has a gradient catastrophe for the studied initial data. The video shows the solutions for 𝛿 = 0.1 and the initial data

u(x,0) = sech^2(x).


See 1304.6513 for references and further details.