The so called "characteristics" of a partial differential equations (PDE) are curves in the [math](x,t)[/math]-plane along which the solution [math]u(x,t)[/math] of the PDE is constant. In the special case of a conservation law (demonstrated here) the characteristics are straight lines.
Experiments: [list] [*] Increase the time [math]T[/math] and see if characteristics cross. Decrease number of characteristics to get a clearer look. [*] Explain using the definition of the characteristics: What happens to [math]u(x,t)[/math] at the point of intersection? [*] Enter a new initial profile [math]u_0(x)[/math]: How does the slope of [math]u_0(x)[/math] affect the characteristics? [*] Change the flow function [math]f(u)[/math]: Try different convex (e.g. [math]u^2[/math]) and concave (e.g. [math]-u^2[/math]) functions and observe the behavior of the characteristics. [/list]