Soliton solutions to the nonlinear Schrödinger equation

Nonlinear science is one of the most important research fields in recent years. In this fieldnonlinear evolution equations are often presented to explain the motion of isolated waves,localized in a small part of space, in many fields such as nonlinear optics, plasma physics,optical fibers, chemical physics optical fibers, chemical physics, etc. In this paper by usingthe Backlund transformation method, we find bright and dark solitary wave solutions tothe higher-order nonlinear Schrödinger equation with the third-order and fourth-orderdispersion and the cubic-quintic nonlinear terms, describing the propagation of extremelyshort pulses.

Keywords:

soliton solutions , Backlundmethod , Riccati equation , higher-order dispersive cubicquinticnonlinear Schrödingerequation.