# Highly Dispersive Optical Solitons of an Equation with Arbitrary Refractive Index

*2020, Volume 25, Number 6, pp. 537-543*

Author(s):

**Kudryashov N. A.**

A nonlinear fourth-order differential equation with arbitrary refractive index for
description of the pulse propagation in an optical fiber is considered. The Cauchy problem for
this equation cannot be solved by the inverse scattering transform and we look for solutions
of the equation using the traveling wave reduction. We present a novel method for finding
soliton solutions of nonlinear evolution equations. The essence of this method is based on the
hypothesis about the possible type of an auxiliary equation with an already known solution. This
new auxiliary equation is used as a basic equation to look for soliton solutions of the original
equation. We have found three forms of soliton solutions of the equation at some constraints
on parameters of the equation.

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