Abstract
Two first-order nonlinear ordinary differential equations of the second power are considered. These differential equations are often used for analytical presentation of solitary and periodic waves at description of the various physical processes in nonlinear optics. It is well known that the general solutions of many differential equations can be found taking into account the Weierstrass and Jacobi elliptic functions. However, many researchers believe that using different elliptic functions, different solutions of nonlinear differential equations can be obtained. In this report, we demonstrate that the General solutions of two popular equations that meet many nonlinear wave processes are described by exact formulas via the Jacobi elliptic sine. Exact relations are given for the studied equations relating to the equation for the Jacobi elliptic sine.
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