Inhomogeneous Mixed-boundary value problem for one dimensional nonlinear Schr\"{o}dinger equations via factorization techniques

TL;DR

This paper investigates the asymptotic behavior of small solutions to the inhomogeneous mixed-boundary value problem for one-dimensional cubic nonlinear Schrödinger equations on the half line, using energy and factorization methods.

Contribution

It introduces new sufficient conditions on initial and boundary data that guarantee the asymptotic behavior of solutions, employing classical energy and factorization techniques.

Findings

Established conditions for asymptotic behavior of solutions.

Applied factorization techniques to boundary value problems.

Provided insights into the long-term dynamics of nonlinear Schrödinger equations.

Abstract

We consider the inhomogeneous Mixed-boundary value problem for the cubic nonlinear Schr\"{o}dinger equations on the half line. We present sufficient conditions of initial and boundary data which ensure asymptotic behavior of small solutions to equations by using the classical energy method and factorization techniques