The authors study the numerical computation of nonlinear dispersive waves by the method of lines. They find that adapting the mesh is crucial to the effective solution of the partial differential equation when the waves exhibit sharp changes.

A fixed mesh is used for a fixed number of steps, with an implicit Runge-Kutta method. The mesh is then equi-distributed and regularized. Initial values on the new mesh are obtained by cubic spline interpolation, and the cycle is repeated. The authors find that some ways of approximating higher derivatives in space are more effective than others.