# Entire solutions originating from three fronts to a two-dimensional nonlocal periodic lattice dynamical system

## TL;DR

This paper investigates entire solutions of a two-dimensional nonlocal periodic lattice dynamical system, introducing new solutions originating from three fronts under specific conditions, expanding understanding of complex wave interactions.

## Contribution

It introduces two novel types of entire solutions originating from three fronts, constructed using auxiliary functions and super- and sub-solutions, extending previous work on merging-front solutions.

## Key findings

- Established existence of new entire solutions from three fronts
- Used auxiliary rational functions to construct solutions
- Extended prior results on merging-front solutions

## Abstract

This paper is concerned with the entire solutions of a two-dimensional nonlocal periodic lattice dynamical system. With bistable assumption, it is well known that the system has three different types of traveling fronts. The existence of merging-front entire solutions originating from two fronts for the system have been established by Dong, Li \& Zhang [{\it Comm. Pur Appl. Anal.}, {\bf17}(2018), 2517-2545]. Under certain conditions on the wave speeds, and by some auxiliary rational functions with certain properties to construct appropriate super- and sub solutions of the system, we establish two new types of entire solutions which originating from three fronts.