Computation of the direct scattering transform for the nonlinear Schrödinger equation
The paper presents a numerical algorithm for determining the direct scattering transform of a narrow-banded wave train, described by the nonlinear Schrödinger equation. The direct scattering transform may be interpreted as the nonlinear Fourier spectrum of the complex envelope function of the wave train. Connections to previous numerical approaches are done. The approach is generalized to include several nonlinear wave equations as the Korteweg- de Vries, sine-Gordon and sinh-Gordon equations.
scientific article; zbMATH DE number 98368
scientific article