Solitons, breathers and rogue waves for a sixth-order variable-coefficient nonlinear Schrodinger equation in an ocean or optical fiber

Under investigation in this paper is a sixth-order variable-coefficient nonlinear Schrodinger equation in an ocean or optical fiber. Through the Darboux transformation (DT) and generalized DT, we obtain the multi-soliton solutions, breathers and rogue waves. Choosing different values of alpha(x), beta(x), gamma(x) and delta(x), which are the coefficients of the third-, fourth-, fifth-and sixth-order dispersions, respectively, we investigate their effects on those solutions, where x is the scaled propagation variable. When alpha(x), beta(x), gamma(x) and delta(x) are chosen as the linear, parabolic and periodic functions, we obtain the parabolic, cubic and quasi-periodic solitons, respectively. Head-on and overtaking interactions between the two solitons are presented, and the interactions are elastic. Besides, with certain values of the spectral parameter lambda, a shock region between the two solitons appears, and the interaction is inelastic. Interactions between two kinds of the breathers are also studied, and we find that the interaction regions are similar to those of the second-order rogue waves. Rogue waves are split into some first-order rogue waves when alpha(x), beta(x), gamma(x) and delta(x) are the periodic or odd-numbered functions.