ABSTRACT
The nonlinear Schrödinger equation (NLSE) is a ubiquitous model for wave evolution in the presence of dispersion and self-phase modulation. It is applicable in fields ranging from oceanography and optics to ionospheric wave beam propagation, and, more generally, describes the evolution of slowly varying quasi-monochromatic wave packets in weakly nonlinear media. Amid numerous extensions and improvements of the model, the Ablowitz– Ladik equation takes the NLSE a step further in asking how nonlinear waves would evolve under the same effective physics but in a discontinuous periodic lattice, such as a fiber array or electronic circuit consisting of repeated elements. Continuous NLSE solutions of third order and beyond are hard to find in simple analytic form due to their complexity, rendering the intuitive direct method limited in its use. For the continuous case, the NLSE supports second-order rogue wave triplet solutions, where three constituent peaks are located equidistantly on a circle.
