# Solitary Wave Formation under the Interplay between Spatial Inhomogeneity and Nonlocality

## TL;DR

This paper investigates how spatial inhomogeneity and nonlocal nonlinearities interact to influence the formation and propagation of solitary waves, revealing conditions for different wave types and their potential for advanced applications.

## Contribution

It provides analytical conditions for solitary wave existence considering inhomogeneity and nonlocality, and explores their dynamic behaviors through numerical simulations.

## Key findings

- Existence of discrete Bright SW and continuous Kink SW families.
- Stable and oscillatory propagation regimes identified.
- Transformations between different SW types demonstrated.

## Abstract

The presence of spatial inhomogeneity in a nonlinear medium restricts the formation of Solitary Waves (SW) on a discrete set of positions whereas a nonlocal nonlinearity tends to smooth the medium response by averaging over neighboring points. The interplay of these antagonistic effects is studied in terms of SW formation and propagation. Formation dynamics is analyzed under a phase space approach and analytical conditions for the existence of either discrete families of Bright SW or continuous families of Kink SW are obtained in terms of Melnikov's method. Propagation dynamics are studied numerically and cases of stable and oscillatory propagation as well as dynamical transformation between different types of SW are shown. The existence of different types and families of SW in the same configuration, under appropriate relations between their spatial width and power with the inhomogeneity and the nonlocality parameters, suggests an advanced functionality of such structures that is quite promising for applications.