A SYSTEM OF INHOMOGENEOUS NLS ARISING IN OPTICAL MEDIA WITH A χ(2) NONLINEARITY, PART II: STABILITY OF STANDING WAVES

Van Duong Dinh; Amin Esfahani

doi:10.3934/dcdsb.2024161

A SYSTEM OF INHOMOGENEOUS NLS ARISING IN OPTICAL MEDIA WITH A χ⁽²⁾ NONLINEARITY, PART II: STABILITY OF STANDING WAVES

Van Duong Dinh, Amin Esfahani

School of Sciences and Humanities

UMPA (UMR 5669)

Research output: Contribution to journal › Article › peer-review

Abstract

We study the inhomogeneous nonlinear Schrödinger system (Formula presented). We employ variational analysis to establish the existence and qualitative properties of ground states associated with the system. The limiting behavior of positive radial ground states as α approaches zero is investigated using the mountain-pass energy method. Additionally, we explore the stability and instability of ground state standing waves. By relaxing the condition of radiality for ground states, we obtain significantly stronger instability results compared to those for the system of NLS.

Original language	English
Pages (from-to)	2209-2232
Number of pages	24
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	30
Issue number	7
DOIs	https://doi.org/10.3934/dcdsb.2024161
Publication status	Published - Jun 2025

Keywords

blow-up
ground state
Inhomogeneous nonlinear Schrödinger system
stability

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.3934/dcdsb.2024161

Cite this

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title = "A SYSTEM OF INHOMOGENEOUS NLS ARISING IN OPTICAL MEDIA WITH A χ(2) NONLINEARITY, PART II: STABILITY OF STANDING WAVES",

abstract = "We study the inhomogeneous nonlinear Schr{\"o}dinger system (Formula presented). We employ variational analysis to establish the existence and qualitative properties of ground states associated with the system. The limiting behavior of positive radial ground states as α approaches zero is investigated using the mountain-pass energy method. Additionally, we explore the stability and instability of ground state standing waves. By relaxing the condition of radiality for ground states, we obtain significantly stronger instability results compared to those for the system of NLS.",

keywords = "blow-up, ground state, Inhomogeneous nonlinear Schr{\"o}dinger system, stability",

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N2 - We study the inhomogeneous nonlinear Schrödinger system (Formula presented). We employ variational analysis to establish the existence and qualitative properties of ground states associated with the system. The limiting behavior of positive radial ground states as α approaches zero is investigated using the mountain-pass energy method. Additionally, we explore the stability and instability of ground state standing waves. By relaxing the condition of radiality for ground states, we obtain significantly stronger instability results compared to those for the system of NLS.

AB - We study the inhomogeneous nonlinear Schrödinger system (Formula presented). We employ variational analysis to establish the existence and qualitative properties of ground states associated with the system. The limiting behavior of positive radial ground states as α approaches zero is investigated using the mountain-pass energy method. Additionally, we explore the stability and instability of ground state standing waves. By relaxing the condition of radiality for ground states, we obtain significantly stronger instability results compared to those for the system of NLS.

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KW - ground state

KW - Inhomogeneous nonlinear Schrödinger system

KW - stability

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