On soliton (in-)stability in multi-dimensional cubic-quintic nonlinear Schrödinger equations

2020/12/21 by Rémi Carles, Christian Klein, Carles, R. +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2012.11637

openalex publication_date 2020/12/21 · openalex created_date 2021/01/05 · openalex updated_date 2026/07/28

Abstract

We consider the nonlinear Schrödinger equation with a focusing cubic term and a defocusing quintic nonlinearity in dimensions two and three. The core of this article is the notion of stability of solitary waves. We recall the two standard notions of orbital stability in the context of nonlinear Schrödinger equations, and show that they must be considered as independent from each other. We investigate numerically the notion of orbital stability of ground states in the radially symmetric case, confirming existing conjectures or leading to new ones.

Citations

• Solitons and Scattering for the Cubic–Quintic Nonlinear Schrödinger Equation on ℝ³ R 3
• Uniqueness and non-degeneracy for a nuclear nonlinear Schr "odinger\n equation
• Orbital stability of standing waves for some nonlinear Schr�dinger equations
• Nonlinear Schr�dinger equations and sharp interpolation estimates
• A MATLAB differentiation matrix suite
• The double-power nonlinear Schr "odinger equation and its\n generalizations: uniqueness, non-degeneracy and applications

Cited by

• Numerical study of transverse (in-)stability of solitary waves in the cubic-quintic nonlinear Schrödinger equation

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