I am attempting to numerically integrate the KdV equation:
u_t + u u_x + u_xxx = 0
As you can see, it is nonlinear. I start with some initial profile u[x,0] = f[x] where f[x] is PERIODIC (such as f[x] = cos[x]), and try to see how it evolves. My question is: is there any way to use PERIODIC BOUNDARY CONDITIONS on NDSolve? Usually, when solving a PDE with NDSolve, one specifies BC like u[0,t]=u[1,t]=0 or something like that. I want to specify simply that u[0,t]==u[1,t]. By the way, I have trouble integrating the KdV even with ordinary BC. I hope its not impossible to do the KdV with Mathematica. I don't look forward to writing a C program for this monster!