Optical solitons and stability regions of the higher order nonlinear Schrodinger's equation in an inhomogeneous fiber

This paper concerns with the integrability of variable coefficient fifth order nonlinear Schrodinger's equation describing the dynamics of attosecond pulses in inhomogeneous fibers. Variable coefficients incorporate varying dispersion and nonlinearity which are of physical significance in considering the nonuniform boundaries of fibers as well as the inhomogeneities of the media. The well-known exp(-phi(s))- expansion method is used to retrieve singular and periodic solitons with the aid of symbolic computation. The structures of the obtained solutions are discussed along with their existence criteria. Moreover, the modulation instability analysis is carried out to identify the instability regions. A dispersion relation is extracted between wave number and frequency. The optimal value of the frequency is found for the occurrence of the instability. A detailed discussion of the results is also given along with graphics.

Automated summary

This paper discusses the integrability of a variable coefficient fifth order nonlinear Schrödinger's equation that describes the dynamics of attosecond pulses in inhomogeneous fibers. The use of variable coefficients allows for the consideration of nonuniform boundaries and media inhomogeneities. The well-known exp(-phi(s)) expansion method is employed to obtain singular and periodic solitons, and their structures and existence criteria are discussed. Modulation instability analysis and dispersion relation extraction are also performed, and comprehensive discussions and graphics are provided.