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Mathematical model of propagation pulse in optical fiber with power nonlinearities

An nonlinear fourth-order equation for describing the pulse propagation in an optical fiber is considered. Equation generalizes a number of well-known mathematical models in nonlinear media. A characteristic feature of the equation is that when describing the envelope of a wave packet, an arbitrary power can be taken for changing the amplitude and width of the pulse. To find exact solutions that traveling wave reduction is used to nonlinear ordinary differential equation. We also present a method for constructing exact solutions using a generalized ordinary first-order differential equation of the second degree as an auxiliary equation. It is shown that the equation under consideration has exact solutions in the form of periodic and solitary waves, which are expressed in terms of the Weierstrass and the Jacobi elliptic functions. Special cases of equation are presented. Periodic and solitary waves of the equation are demonstrated.


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