Relationships between the choice of the positive and negative frequency expression of optical waves, adoption of Fourier transformation form and form of nonlinear Schrödinger equation are discussed. The generally accepted form of nonlinear Schrödinger equation is the result of choosing the negative frequency expression. In accord with the negative frequency expression, the form of Fourier transformation cannot be chosen at will. When the nonlinear Schrödinger equation is solved using numerical methods based on Fourier transformation, the form of fast Fourier transformation must be paid attention in the programming languages used. In most programming languages, the adopted forms of fast Fourier transformation and inverse transformation are opposite to the forms adopted in nonlinear optics. It is also pointed out that some related numerical errors existed in some references.