Conservation laws, -fold Darboux transformation, -dark-bright solitons and the th-order breathers of a variable-coefficient fourth-order nonlinear Schrodinger system in an inhomogeneous optical fiber

Optical fiber communication system is one of the core supporting systems of the modern internet age. For the simultaneous propagation of nonlinear waves in an inhomogeneous optical fiber, in this work, a coupled variable-coefficient fourth-order nonlinear Schrodinger system is studied. Infinitely-many conservation laws and ������-fold Darboux transformation (DT) based on the existing Lax pair under certain constraints are derived, where ������is a positive integer. Via the ������-fold DT, the ������-dark-bright soliton and ������th-order breather solutions under certain constraints are given. Interactions between the two dark-bright solitons are depicted graphically when the dispersion coefficient in that system, ������1(������), and the group velocity dispersion coefficient in that system, ������(������), are the constants and periodic functions, where ������means the normalized retarded time. It is found that the velocities of the two dark-bright solitons increase as ������1(������) and ������(������) increase when ������1(������) and ������(������) are the constants. Interactions between the two breathers are presented graphically.