Soliton and breather solutions for the seventh-order variable-coefficient nonlinear Schrödinger equation

In this article, a seventh-order variable-coefficient nonlinear Schrödinger equation is investigated in an optical fiber. By means of the Darboux transformation, soliton and breather solutions are derived and the following results are attained: (i) The one soliton and interactions of two solitons are presented, whose basic structures are parabolic-like, cubic and periodical-oscillating solitons; (ii) The first-order breather and interactions between the two breathers are studied. Several interesting nonlinear wave patterns such as cow-shaped breathers and breathers with periodic properties are displayed; (iii) The dynamic behaviors of solitons and breather waves are affected by the variable coefficients.