Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations

The scattering data of the considered inverse scattering problems (ISPs) are described completely. Solving the associated IVP or IBVP for the nonlinear evolution equations (NLEEs) is carried out step by step. Namely, the NLEE can be written as the compatibility condition of two linear equations. The inverse scattering method (ISM) to solving the IVPs or IBVPs for NLEEs is consistent. It is effectively embedded in the schema of the ISM. Application of ISM to solving the NLEEs is effectively embedded in the scheme of the ISM.