# Light meets water in nonlocal media: Surface tension analogue in optics

## TL;DR

This paper establishes an optical analogue of surface tension in shallow water waves through a nonlocal nonlinear Schrödinger model, revealing how nonlocality influences wave dispersion and reduces to KP equations.

## Contribution

It introduces a parameter linking nonlocality to surface tension effects in optics and derives KP equations from the NLS model for different nonlocality regimes.

## Key findings

- Identification of a surface tension analogue in optics
- Derivation of KP equations from the NLS model
- Demonstration of nonlocality's effect on wave dispersion

## Abstract

Shallow water wave phenomena find their analogue in optics through a nonlocal nonlinear Schr\"odinger (NLS) model in $(2+1)$-dimensions. We identify an analogue of surface tension in optics, namely a single parameter depending on the degree of nonlocality, which changes the sign of dispersion, much like surface tension does in the shallow water wave problem. Using multiscale expansions, we reduce the NLS model to a Kadomtsev-Petviashvilli (KP) equation, which is of the KPII (KPI) type, for strong (weak) nonlocality.