Asymmetric localized states in periodic potentials with a domain wall-like Kerr nonlinearity

TL;DR

This paper investigates novel asymmetric localized states in one-dimensional periodic potentials with a domain-wall-like Kerr nonlinearity, demonstrating their existence and stability, with potential applications in Bose-Einstein condensates and optical systems.

Contribution

It introduces new types of asymmetric localized states supported by a domain-wall Kerr nonlinearity in periodic potentials, analyzing their stability and experimental relevance.

Findings

Multiple new asymmetric localized states identified.

Localized states are stable within finite band gaps.

Potential for experimental realization in optical and atomic systems.

Abstract

We study the existence of one-dimensional localized states supported by linear periodic potentials and a domain-wall-like Kerr nonlinearity. The model gives rise to several new types of asymmetric localized states, including single- and double-hump soliton profiles, and multihump structures. Exploiting the linear stability analysis and direct simulations, we prove that these localized states are exceptional stable in the respective finite band gaps. The model applies to Bose-Einstein condensates loaded onto optical lattices, and in optics with period potentials, e.g., the photonic crystals and optical waveguide arrays, thereby the predicted solutions can be implemented in the state-of-the-art experiments.