NUMERICALLY INDUCED EVOLUTION OF NLS SOLITONS: ANALYTICAL SOLUTIONS FOR SCHEMES WITH SECOND-ORDER DISCRETISATION ERRORS

Soliton perturbation theory is used to obtain analytical solutions describing the evolution of NLS solitons, due to numerical discretisation error. Two important implicit numerical schemes (the Crank-Nicolson (CN) scheme and Taha scheme) for the NLS equation, with second-order temporal and spatial discretisation errors, are considered. The solutions for the solitary wave tail are in integral form and an explicit expression is found, for large time. The location of zeros and the location and amplitude of peaks, in the solitary wave tail, are also analytically obtained