Existence of Peregrine Solitons in fractional reaction-diffusion equations

TL;DR

This paper investigates the existence of Peregrine solitons in fractional reaction-diffusion equations using splitting methods, establishing global existence results for different solution characteristics.

Contribution

It introduces a novel analysis of Peregrine solutions in fractional reaction-diffusion equations and combines results for different solution behaviors.

Findings

Existence of Peregrine solutions for fractional reaction-diffusion equations.

Global existence results for solutions with different asymptotic behaviors.

Application of splitting methods to analyze solution existence.

Abstract

In this article, we will analyze the existence of Peregrine type solutions for the fractional diffusion reaction equation by applying Splitting-type methods. These functions that have two main characteristics, they are direct sum of functions of periodic type and functions that tend to zero at infinity. Global existence results are obtained for each particular characteristic, for then finally combining both results.