ABSTRACT
In order to efficiently compute numerical solutions of these equations, it is appealing to resort to an adaptive grid technique that automatically concentrates the spatial nodes in the regions of rapid solution variations (i.e., the wave moving fronts). In this connection, an adaptive grid refinement algorithm based on the equidistribution principle and spatial regularization procedures is implemented and applied to several illustrative problems, including the propagation of a single soliton, the interaction between two solitons, and the bound state of several solitons, and the propagation of a compacton (a soliton with compact support).
