Compactons in Nonlinear Schr\"odinger Lattices with Strong Nonlinearity Management

TL;DR

This paper demonstrates the existence of stable discrete compactons in nonlinear Schrödinger lattices with strong, fast periodic nonlinearity modulation, revealing new nonlinear dispersion effects and potential applications in optical and BEC systems.

Contribution

It introduces a novel mechanism for creating stable compactons via nonlinear dispersion induced by strong nonlinearity management in discrete Schrödinger systems.

Findings

Stable discrete compactons can form dynamically from Gaussian or compact initial data.

Effective inter-well tunneling depends on modulation parameters and field amplitude.

Nonlinear dispersion enables new localized wave structures in optical and BEC arrays.

Abstract

The existence of compactons in the discrete nonlinear Schr\"odinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. In the averaged DNLS equation the resulting effective inter-well tunneling depends on modulation parameters {\it and} on the field amplitude. This introduces nonlinear dispersion in the system and can lead to a prototypical realization of single- or multi-site stable discrete compactons in nonlinear optical waveguide and BEC arrays. These structures can dynamically arise out of Gaussian or compactly supported initial data.