Abstract
Nonlinear fourth-order partial differential equation with non-local nonlinearity for describing pulses in optical fiber is considered. The traveling wave reductions to the equation are used to obtain the real and imaginary parts of nonlinear differential equation. Using the Painlevé analysis to the system of equations it is shown that this system does not have the general solution with four arbitrary constants. However the equation can have exact solution with the smaller number of arbitrary constants. Conditions for some parameters of the mathematical model are found for solution of the system of equations. Exact solutions for the system of equations are found by the means of the simplest equation method. Exact solutions are given using the Jacobi elliptic functions.
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