Modulational instability, nonautonomous characteristics and semirational solutions for the coupled nonlinear Schrödinger equations in inhomogeneous fibers

• Effects of the fiber parameters on the modulational instability criterion.
• Nonautonomous characteristics of the higher-order asymmetric breather and RW solutions by the n-fold mDT with variable coefficients.
• Nonautonomous semirational solution in terms of the determinant.

We study the multimode wave propagation in inhomogeneous coupled nonlinear optical fibers modeled by the variable-coefficient coupled nonlinear Schrödinger (vc-CNLS) equations. The effect of the optical parameters on the modulational instability criterion for the vc-CNLS equations is numerically investigated. The higher-order asymmetric breather and rogue wave (RW) solutions are obtained via the n-fold modified Darboux transformation (mDT) with inhomogeneous parameters. The nonautonomous characteristics of these solutions are discussed including the breather amplification, periodic asymmetric RWs, maintenance of asymmetric RWs, asymmetric RW pair, nonlinear Talbot-like effect and nonlinear tunneling effect. In addition, we derive the semirational solutions of the vc-CNLS equations through improving the Taylor expansion technique in the mDT. Such type of solutions can be used to describe the interactions between the asymmetric RWs and breathers, and explain the formation mechanism of higher-order asymmetric RWs.