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We derive analytical rogue wave solutions of variable-coefficient higher-order nonlinear Schrödinger equations describing the femtosecond pulse propagation via a transformation connected with the constant-coefficient Hirota equation. Then we discuss the propagation behaviors of controllable rogue waves, including recurrence, annihilation, and sustainment in a periodic distributed fiber system and an exponential dispersion decreasing fiber. Finally, we investigate nonlinear tunneling effects for rogue waves.

We derive analytical 3D spatiotemporal similaritons and solitons of the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients.

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