Asymptotic stability of small gap solitons in the nonlinear Dirac\n equations

2010/08/26 by Dmitry E. Pelinovsky, Pelinovsky, Dmitry E., Atanas Stefanov +1 · 2 citations
Mathematics · #Advanced Mathematical Physics Problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1008.4514

Abstract

We prove dispersive decay estimates for the one-dimensional Dirac operator\nand use them to prove asymptotic stability of small gap solitons in the\nnonlinear Dirac equations with quintic and higher-order nonlinear terms.\n

Citations

• Time decay for solutions of Schr�dinger equations with rough and time-dependent potentials
• SELECTION OF THE GROUND STATE FOR NONLINEAR SCHRÖDINGER EQUATIONS

Cited by

• Dispersive estimates of Dirac equations with a domain wall
• On stability of standing waves of nonlinear Dirac equations

Related

• Decay of solutions of nonlinear Dirac equations
• Asymptotic stability of small solitons in the discrete nonlinear Schrodinger equation in one dimension
• Linear instability of nonlinear Dirac equation in 1D with higher order nonlinearity
• Stability of parametrically driven, damped nonlinear Dirac solitons
• On the Darboux and Birkhoff steps in the asymptotic stability of solitons