On the stability of solitary waves in the NLS system of the third-harmonic generation

DOI10.1007/s13324-023-00862-2zbMath1528.35179arXiv2304.01867OpenAlexW4389890413MaRDI QIDQ6145791

Abba Ramadan, Atanas G. Stefanov

Publication date: 9 January 2024

Published in: Analysis and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2304.01867

zbMATH Keywords

solitary wavesspectral stabilitysystems of nonlinear Schrödinger equationsinstability by blow up

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Soliton equations (35Q51) Traveling wave solutions (35C07) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Cites Work

• Spectral and dynamical stability of nonlinear waves
• On a Schrödinger system arizing in nonlinear optics
• Lyapunov stability of ground states of nonlinear dispersive evolution equations
• Sharp conditions for scattering and blow-up for a system of NLS arising in optical materials with χ³ nonlinear response
• Instability, index theorem, and exponential trichotomy for Linear Hamiltonian PDEs
• Strong Instability of Standing Waves for Nonlinear Schrödinger Equations with Harmonic Potential
• Inertia law for spectral stability of solitary waves in coupled nonlinear Schrödinger equations
• Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems
• Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems

This page was built for publication: On the stability of solitary waves in the NLS system of the third-harmonic generation