Bright-dark solitary waves, complexitons, Guassian solitons, and traveling wave solitons of the second-order non-linear Schrödinger equation with spatial and temporal dispersion

Abstract

In this paper, we consider the non-linear Schrödinger equation in fibers with the presence of group velocity dispersion, selfphase modulation and second-order dispersion terms. Using the ansatz method, we derive its bright, dark, complexitons, Gaussian, and traveling wave solitons, respectively. Moreover, we provide the graphical analysis of some solutions in order to better understand their dynamical behavior.

Keywords:

• The second-order non-linear Schrödinger equation
• bight soliton solution
• dark soliton solution
• complexitons solution
• Gaussian solution
• traveling wave solution

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Research and Practice of Educational Reform for Graduate students in China University of Mining and Technology [grant number YJSJG_2017_049], the “Qinglan Engineering project” of Jiangsu Universities, the National Natural Science Foundation of China [grant number 11301527], [grant number 51522902], [grant number 51379033] and [grant number 51579040], the 973 program [grant number 2013CB036101], and the General Financial Grant from the China Postdoctoral Science Foundation [grant number 2015M570498] and [grant number 2017T100413].