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Soliton solutions of non-linear NLS and KdV equations are related tocompatibility condition between matrices M and H describing the movement of anauxilary function Psi in the x,t plane with a zero curvature condition.Non-linear equation for a function u is obtained by the compatibility equationwhere the matrix elements of M and H include only functions of u and itsderivatives. By solving the equations of motion for Psi a soliton solution foru is obtained. Explicit calculations are made with two-dimensional andone-dimensional wave functions Psi for the NLS and KdV solitons,correspondingly.

Soliton solutions of non-linear Schrodinger (NLS) and Korteweg de Vries (KdV) equations related to zero curvature in the x,t plane