Abstract
The present paper focuses on a specific method for solving systems of differential equations with application in nonlinear optics. The basic system is presented by two coupled nonlinear differential equations, written in dimensionless form, which govern the propagation of light pulses in optical fibers. The mathematical algorithm is described in detail in the article. The system is analytically solved. The obtained solutions of the equations are in the form of special functions - Jacobi elliptic delta function. They determine the periodical energy exchange between light pulses. The mathematical method can be applied for pulses with arbitrary initial intensities, generalized phase and wave number mismatch.
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