Perturbation expansion and Nth order Fermi golden rule of the nonlinear Schrödinger equations

2007/05/01 by Zhou Gang, Gang Zhou · 4 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Advanced Mathematical Physics Problems #Nonlinear Photonic Systems

paper · doi:10.1063/1.2716971

Abstract

In this paper we consider generalized nonlinear Schrödinger equations with external potentials. We find the expressions for the fourth and the sixth order Fermi golden rules (FGRs), conjectured in Gang and Sigal [Rev. Math. Phys. 17, 1143–1207 (2005); Geom. Funct. Anal. 16, No. 7, 1377–1390 (2006)]. The FGR is a key condition in a study of the asymptotic dynamics of trapped solitons.

Citations

• Non-linear wave and Schrödinger equations
• Resonances, radiation damping and instabilitym in Hamiltonian nonlinear wave equations
• Existence of solitary waves in higher dimensions
• Asymptotic dynamics of nonlinear Schrödinger equations: Resonance‐dominated and dispersion‐dominated solutions
• Nonlinear scalar field equations, I existence of a ground state

Cited by

• A Resonance Problem in Relaxation of Ground States of Nonlinear Schrodinger Equations
• On instability of excited states of the nonlinear Schrödinger equation
• A survey on asymptotic stability of ground states of nonlinear Schrodinger equations II
• The Hamiltonian structure of the nonlinear Schr "odinger equation and\n the asymptotic stability of its ground states

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• Perturbation Expansion and N-th Order Fermi Golden Rule of the Nonlinear Schrödinger Equations
• A survey on asymptotic stability of ground states of nonlinear Schrodinger equations II
• A note on the Fermi Golden Rule constant for the pure power NLS
• On the asymptotic stability of ground states of the pure power NLS on the line at 3rd and 4th order Fermi Golden Rule
• On instability of some approximate periodic solutions for the full nonlinear Schrödinger equation