Waves like Tsunami and their destructive effects are well known to mankind.

Waves with similar features but with less dramatic effect can be created inside an optical fiber. These waves can be exploited for high speed long distance optical communication. In 1991 the optical solitons inside an optical were experimentally demonstrated.

The deployment of soliton based optical communication systems still are not feasible but the technology is progressing to make the solitonic communication a reality.

In the presence of non-linearity and dispersion, there is possibility of undistorted pulse propagation for infinite distance.

Let define normalized distance and normalized time as

The Schrodinger equation with dispersion and non-linearity, can be written as

Where the parameter is defined as

The solution to the NSE in this case is the Soliton. For , we get the fundamental soliton and for higher values of we get the higher order solitons. Of course, the higher order solitons need higher optical power.

The solution of the NSE for the fundamental soliton is

It indicated that if a secant hyperbolic pulse is launched inside an optical fiber, it can travel undistorted for infinite distance (of course in absence of loss).

The fundamental soliton has a very special wave shape, the secant hyperbolic function .

Let us see how the two frequency chirps, one due to non-linearity and other due to the dispersion get cancelled for secant hyperbolic pulse shape.

The NSE due for only non-linear term is

The non-linear phase is

The NSE due only anomalous dispersion can be written as

The phase due to dispersion is

The sum of the non-linear and the dispersion phase is

Independent of time.

The resultant frequency chirp therefore is zero and the pulse spectrum and consequently its shape remains unchanged.