Abstract
This paper deals with numerical solutions of nonlinear evolution equations solvable by the inverse scattering transform (IST), namely the nonlinear Schrodinger (NLS), the Korteweg-de Vries (KdV) and the modified Korteweg-de Vries (MKdV) equations. These equations describe a wide class of physical phenomena (Ablowitz and Segur, 1981). Comparisons between schemes constructed by methods related to the IST and certain other known numerical methods (a) finite difference and (b) finite Fourier (pseudo-spectral) methods are obtained. Experiments have shown that the IST schemes compare very favorably with known numerical methods. In this paper a summary of the results of the performance of the 1ST schemes for the NLS and KdV equations will be discussed, and a new results of the performance of the IST scheme for the MKdV equation will be presented.
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