Non-Hermitian Origin of Surface Peregrine Soliton and Its Topological Signatures (2509.05493v1)

Abstract: A wide range of dynamic wave localization phenomena manifest underlying intricate physical effects in the diverse areas of physics, and in particular, in optics and photonics, which often bear signatures of implicit nontrivial wave structures. A Peregrine soliton that has a complex wave structure draws particular interest in nonlinear wave optics because of its space-time localization and prototypical analogy of the extreme form of wave localization. In the PT variant of the standard NLSE, we show nontrivial wave coupling of the initial excitations, giving rise to intriguing complex wave interaction in the unbroken and broken regimes of PT symmetry at an optical interface of a composite complex optical system. In particular, a surface Peregrine soliton mode is found to exist at the interface between two optical media characterized by distinct nonlinear and dispersive properties. Remarkably, it yields stable wave propagation in the unbroken PT regime despite discontinuities in the optical properties, and enhanced surface wave localization in the broken PT phase. We show that such a surface mode emanates from the interplay between the non-Hermitian pseudo-self-induced PT potential and a nonlinearity-dispersion engineering scheme of the composite optical system which, in effect, forms a non-Hermitian topological domain wall at the interface between two distinct optical media. The topological signatures of the surface Peregrine soliton mode are discussed. This work sheds light on the wave localization in the non-Hermitian optical wave systems in general, and illustrates, in particular, for the first time, the existence of a surface Peregrine soliton mode at the cross-field synergistic point of nonlinear optics, non-Hermitian physics, and topological wave phenomena.