This nonlinear partial differential equation models how the envelope and phase of light pulse changes when propagating through an optical fiber, when taking power attenuation α, Group Velocity Dispersion β and waveguide nonlinearity γ causing Self-Phase Modulation (SPM) into account.

Pulses launched into an optical fiber will evolve according to the NLSE When \( \beta \) is negative (anormalous dispersion), the term representing Group Velocity Dispersion (GVD) : \( -i\frac{\beta}{2} \frac{\partial^2 A}{\partial T^2} \) will cause a positive (blue) chirp in the front and a negative (red) chirp in the back. Similarly, the term representing self-phase modulation (SPM) : \( i\gamma |A|^2 A \) will cause a red chirp in the front and a blue chirp in the back. Since the chirp caused by GVD depends on the 2nd derivative (curvature) of the pulse, while the oppositely signed chirp of SPM depends on the squared amplitude of the pulse, we can ask the following question: "Is there some pulse envelope, where the effects of GVD and SPM exactly cancel out, causing the pulse to retain its shape as it propagates?" Such a pulse is called a "soliton". The Sech Pulse is the pulse shape that corresponds to a Fundamental soliton.