Investigation of time-dependent Paraxial Equation with an Analytical Method

Abstract

In this article, we describe the unified auxiliary equation method to obtain solutions with the help of the jacobi elliptic sine and cosine functions. We search for new solutions by applying this method to the dimensionless time-dependent Paraxial equation used in mathematical optics. We get the solutions found for the equation as jacobi elliptic, dark, singular solutions. Different solutions provide solid interpretation in different aspects of related subjects such as mathematical physics, mathematical optics. All solutions are verified by substituting them into the original equation with the help of computere software. Also, we provide graphs for some solutions.