Variable coefficient higher-order nonlinear Schrödinger type equations and their solutions

Abstract

In this communication we focus on certain higher-order partial differential equations of the nonlinear Schrödinger type with variable coefficients. By using a traveling wave reduction we obtain the general solution for the envelope in terms of the Jacobi elliptic sine function. The time dependence of the traveling wave coordinate and phase are explicitly determined as functions of the variable coefficients appearing in the equations. The equations investigated display cubic and fourth-order dispersion terms as well as higher nonlinearity and their constant coefficient versions have been the subject of a number of recent studies.