Solitons and quasi-periodic behaviors in an inhomogeneous optical fiber

In this paper, a fifth order variable coefficient nonlinear Schrodinger equation for the attosecond pulses in an inhomogeneous optical fiber is studied. With the aid of auxiliary functions, we obtain the variable-coefficient Hirota bilinear equations and corresponding integrable constraints. Under those constraints, we obtain the Lax pair, conservation laws, one-, two- and three-soliton solutions via the Hirota method and symbolic computation. Soliton structures and interactions are discussed: (1) For the one soliton, we discuss the influence of the group velocity dispersion term alpha(x) and fifth-order dispersion term delta(x) on the velocities and structures of the solitons, where x is the normalized propagation along the fiber, and derive a constraint contributing to the stationary soliton; (2) For the two solitons, we analyze the interactions between them with different values of alpha(x) and delta(x), and derive the quasi-periodic formulae for three cases of the bound states: When alpha(x) and delta(x) are the linear functions of x, quasi-periodic attraction and repulsion lead to the redistribution of the energy of the two solitons, and ratios among the quasi-periods are derived; When alpha(x) and delta(x) are the quadratic functions of x, the ratios among them are also obtained; When alpha(x) and delta(x) are the periodic functions of x, bi-periodic phenomena are obtained; (3) For the three solitons, including the parabolic, cubic, periodic and stationary structures, interactions among them with different values of the alpha(x) and delta(x) are presented. (C) 2016 Elsevier B.V. All rights reserved.