Solitons for a generalized sixth-order variable-coefficient nonlinear Schrödinger equation for the attosecond pulses in an optical fiber

In this paper, under investigation is a sixth-order variable-coefficient nonlinear Schrödinger equation, which could describe the attosecond pulses in an optical fiber. Based on the self-similarity transformation and Hirota method, one- and two-soliton solutions are obtained under certain constraints. Investigation shows that the velocities and shapes of the solitons and bound solitons are both affected by the sixth-order dispersion term, and the maximum intensities of the solitons and bound solitons increase when the gain function is positive and decrease when the gain function is negative, otherwise the periodicity of the bound solitons is destroyed when the gain function is not 0.