Solitons, breather and bound waves for a generalized higher-order nonlinear Schrödinger equation in an optical fiber or a planar waveguide

In this paper, a generalized higher-order nonlinear Schrödinger equation with variable coefficients is investigated, which could describe the attosecond pulses in an optical fiber or a continuous wave beam in a planar waveguide. Based on the transformation, symbolic computation and Hirota method, the new bilinear forms, one-, two-, three-soliton solutions are obtained under certain constraints. We see that: i) the fifth-order dispersion may affect the soliton velocity as well as the velocities of the breathers and bound solitons; ii) the fifth-order dispersion may influence the shapes of the breathers and bound solitons; iii) the gain function has an impact on the intensities of the solitons, breathers and bound solitons; iv) the gain function may change the breathers’ and bound solitons’ periods and v) the solitons can change into the breathers under the influence of a certain gain function.