Abstract
We present a few of higher-order partial differential equations which can be used for description of propagation pulses in optical fibers. The main criterion for the construction of equations was the presence of soliton solutions of a certain form. Using the first-order nonlinear differential equation, which can be found by means of traveling wave reduction from the nonlinear Schrödinger equation, we construct nonlinear ordinary differential equations of the fourth and sixth order. Taking into account these nonlinear ordinary differential equations, we construct partial differential equations for describing the propagation pulses in an optical fiber. It is characteristic that all constructed high-order dispersive equations have the same exact solutions, which are expressed via the elliptic functions.
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