Solutions of the two-wave interactions in quadratic nonlinear media

TL;DR

This paper develops a mathematical framework for analyzing two-wave soliton interactions in quadratic nonlinear media, proving existence and uniqueness of solutions and providing an accurate iterative approximation method.

Contribution

It introduces a rigorous approach using Schauder's fixed point theorem and offers a new iterative algorithm for approximate solutions in quadratic nonlinear media.

Findings

Existence of two-wave soliton solutions is proven.

Uniqueness of the solutions is established.

An accurate iterative method for approximating solutions is developed.

Abstract

In this paper, we propose a reliable treatment for studying the two-wave (symbiotic) solitons of interactions in nonlinear quadratic media. We investigate Schauder's fixed point theorem for proving the existence theorem. Additionally, the uniqueness solution for this system is proved. Also, a highly accurate approximate solution is presented via an iteration algorithm.