Survey on global existence in the nonlinear Dirac equations in one spatial dimension (Harmonic Analysis and Nonlinear Partial Differential Equations)
Year: 2011
Type: article
Abstract: We consider the nonlinear Dirac equations in one spatial dimension and review various results on global existence of solutions in H^{1} .Depending on the character of the nonlinear terms, existence of the large-norm solutions can be extended for all times.Global existence of the small-norm solutions is proved for the most general nonlinear Dirac equations with cubic and higher-order nonlinear terms.Integrability is used to find conditions that no solitons occur in the Cauchy problem for the massive Thirring model with small initial data in L^{2}.we show that small initial data in L^{2} are associated to purely continuous spectrum of the Lax operator and admits no solitons in the long-time asymptotics.
Author: Dmitry E. Pelinovsky
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1603391748