Exact solutions to the nonlinear Schr\"odinger equation with time-dependent coefficients

TL;DR

This paper employs the trial function method to derive exact solutions for high-order nonlinear Schrödinger equations with time-dependent coefficients, modeling ultrashort light pulse propagation in nonlinear fibers.

Contribution

It introduces a novel application of the trial function method to find exact solutions for complex high-order nonlinear Schrödinger equations with time-dependent coefficients.

Findings

Derived Jacobi elliptic function solutions

Obtained solitary wave solutions

Found rational function solutions

Abstract

In this paper, the trial function method is employed to find the exact solutions for high-order nonlinear Schr\"odinger equations with time-dependent coefficients. This system describes the propagation of ultrashort light pulses in nonlinear fibers, with self-steepening and self-frequency shift effects. As a result, we derive a range of exact solutions which include Jacobi elliptic function solutions, solitary wave solutions, and rational function solutions.