A solution spectrum of the nonlinear Schr�dinger equation. II

Abstract

The soliton solutions of the formψ=A/coshkx andψ=B tanhkx of the nonlinear Schrodinger equation have been considered with respect to many problems. In this paper, it is shown that the nonlinear Schrodinger equation also possesses a solution manifold that generalizes the above soliton functions and provides a discrete spectrum of eigenfunctions and eigenvalues. With the help of a slight modification of these eigenfunctions, it is possible to extend them to the relativistic case, where they become solutions of a nonlinear Klein-Gordon equation associated with a discrete mass spectrum.