We study the infinite integrable nonlinear Schrödinger equation hierarchy beyond the Lakshmanan-Porsezian-Daniel equation which is a particular (fourth-order) case of the hierarchy. In particular, we present the generalized Lax pair and generalized soliton solutions, plane wave solutions, Akhmediev breathers, Kuznetsov-Ma breathers, periodic solutions, and rogue wave solutions for this infinite-order hierarchy. We find that “even- order” equations in the set affect phase and “stretching factors” in the solutions, while “odd-order” equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are always complex.

We explore the concept of passive-feedback lasers (PFLs) for direct signal modulation at 40 Gb/s. Based on numerical simulation and bifurcation analysis, we explain the main mechanisms in these devices that are crucial for modulation at high speed. The predicted effects are demonstrated experimentally by means of correspondingly designed devices. In particular, a significant improvement of the modulation bandwidth at low-injection currents can be demonstrated

We present a multiparameter family of a soliton on a background solution to the Sasa-Satsuma equation. The solution is controlled by a set of several free parameters that control the background amplitude as well as the soliton itself. This family of solutions admits a few nontrivial limiting cases that are considered in detail. Among these special cases is the nonlinear Schr\"odinger equation limit and the limit of rogue wave solutions.