Generalized Fourier transforms for nonlinear systems

Abstract

A simple generalization is presented of the usual Fourier transforms using generalized exponential and Fourier series developed previously for nonlinear systems. The expressions are given in terms of Jacobi elliptic functions in a form as close as possible to the Fourier transform. There is a pair of transforms for each value of the Jacobi parameter m. Simple applications are presented, one of which gives the generalized Yukawa potential and another that gives the generalized Breit–Wigner potential: Both correspond to the generalized Klein–Gordon equation.