Inverse scattering transform

Summary

The inverse scattering transform is a method to solve the initial value problem of some nonlinear evolution equations, such as the Korteweg–De Vries equation. The solution at time $t$ is the potential of a linear spectral problem, such as a Schrödinger operator in one variable. Its scattering data evolve in time by simple explicit formulas, and the potential is then recovered from the data. It plays for these nonlinear equations the role that the Fourier transform plays for linear equations with constant coefficients.