Classes of new exact solutions for nonlinear Schrödinger equations with variable coefficients arising in optical fiber

In this paper, a new modified direct similarity reduction method is considered to find new classes of Jacobi, hyperbolic and periodic wave solutions for both (1 + 1)-dimensional and (2 + 1)-dimensional nonlinear variable coefficients Schrödinger equations (vcNLSE) arising in optical fiber. Additionally, as a conclusion we have arrived in a theorem for both direct reduction and exact solutions to (n + 1)-dimensional vcNLSE. Finally, some physical applications for optical soliton propagation is given joint with figures.