Wellposedness of bounded solutions of the non-homogeneous initial boundary for the short pulse equation

TL;DR

This paper investigates the mathematical well-posedness of bounded solutions for the inhomogeneous initial boundary value problem of the short pulse equation, which models ultra-short light pulse propagation in optical fibers.

Contribution

It establishes the conditions under which solutions to the inhomogeneous short pulse equation are well-posed, advancing the mathematical understanding of this nonlinear model.

Findings

Proved well-posedness of bounded solutions for the inhomogeneous problem

Identified key conditions ensuring solution existence and uniqueness

Enhanced the theoretical foundation for modeling ultra-short light pulses

Abstract

The short pulse equation provides a model for the propagation of the ultra-short light pulse in silica optical fibers It is a nonlinear evolution equation. In this paper the wellposedness of bounded solutions for the inhomogeneous initial boundary value problem associated to this equation is studied.