Integrable equations  We conduct scientific computing on integrable equations aiming to preserve their Hamiltonians and  global/local conservation equations and minimize  the dispersion error.    1. Nonlinear cubic Schrödinger equation in one and two dimensions  2. One-component and two-component Camassa-Holm (CH) equations  3. Degasperis-Procesi equation  4. One-component and two-component Hunter-Saxton equations    We also conduct IST (Inverse Scattering Transform) analysis on one-component Camassa-Holm  equation SCCS Laboratory 2006, all rights reserved Department of Engineering Science and Ocean Engineering, National Taiwan University e-mail : twhsheu@ntu.edu.tw phone : +886-2-3366-5726 address :No.1, Sec. 4, Roosevelt Road, Taipei, Taiwan 106, Republic of China