Novel wave solutions to a generalized third-order nonlinear Schrödinger’s equation

Abstract

Schrödinger’s equation and its variants play an important role in describing many well-known problems in disciplines such as mathematics and physics. Our main concern in this paper is to investigate some novel analytical solutions to a third-order generalized nonlinear Schrödinger’s equation. This equation is used to model the motion of ultra-short pulses in optical fibers. The model also includes several arbitrary parameters that introduce several well-known nonlinear models as its special case. The main achievements of the paper are determined via two efficient methodologies based upon the modified generalized exponential rational function method and a logarithmic transformation approach. In order to better examine the results, three-dimensional diagrams obtained from analytical answers have been attached to the article. These diagrams are useful tools that facilitate a better description of the capabilities of this model. One of the advantages of the method used in this research over some other techniques is that it is possible to adapt the implemented algorithm to solve other complex new problems.