Abstract: We prove that a certain finite difference scheme converges to the weak solution of the Cauchy problem on a finite interval with periodic boundary conditions for the Camassa–Holm equation ut-uxxt+3uux -2uxuxx-uuxxx=0 with initial data u|t=0=u0∈H1([0,1]). Here it is assumed that u-u0''≥0 and in this case, the solution is unique, globally defined, and energy preserving.
Conservation Laws Preprint Server <conservation@math.ntnu.no> 2004-07-22 13:07:16 UTC