On a Method for Constructing Solutions to Equations of Nonlinear Optics

Abstract

The analysis of integrable nonlinear evolutionary equations has shown that these equations can be replaced by others by switching to products and Wronskians of solutions of the original equations. This paper describes the relationship of solutions of equations from the hierarchy of derivative nonlinear Schrödinger equations with solutions of non-local Kadomtsev-Petviashvili equations. The derivative nonlinear Schrödinger equation admits some physical applications, such as the wave propagation of circular polarized nonlinear Alfvén waves in plasmas, weak nonlinear electromagnetic waves in ferromagnetic, antiferromagnetic or dielectric systems under external magnetic fields. Moreover, considered equations can be used for description the transmission of femtosecond pulses in optical fibers. The one-phase solution in elliptic Jacobi functions is given. The paper also presents solutions expressed in terms of hyperbolic and rational functions.