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Stability of solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity

Opened Access Stability of solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity

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Autor: Sihong, Shao
Quintero, Niurka R.
Mertens, Franz G.
Khare, Avinash
Saxena, Avadh
Departamento: Universidad de Sevilla. Departamento de Física Aplicada I
Instituto de Matemáticas de la Universidad de Sevilla (Antonio de Castro Brzezicki)
Fecha: 2014
Publicado en: Physical Review E, 2014, 90 (3), 032915: 1-15
Tipo de documento: Artículo
Resumen: We consider the nonlinear Dirac equation in 1 + 1 dimension with scalar-scalar self interaction g2κ+1(Ψ¯¯¯Ψ)κ+1 and with mass m. Using the exact analytic form for rest frame solitary waves of the form Ψ(x,t)=ψ(x)e−iωt for arbitrary κ, we discuss the validity of various approaches to understanding stability that were successful for the nonlinear Schrödinger equation. In particular we study the validity of a version of Derrick's theorem and the criterion of Bogolubsky as well as the Vakhitov-Kolokolov criterion, and find that these criteria yield inconsistent results. Therefore, we study the stability by numerical simulations using a recently developed fourth-order operator splitting integration method. For different ranges of κ we map out the stability regimes in ω. We find that all stable nonlinear Dirac solitary waves have a one-hump profile, but not all one-hump waves are stable, while all waves with two humps are unstable. We also find that the time tc, it takes for the instability...
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Tamaño: 1.956Mb
Formato: PDF

URI: http://hdl.handle.net/11441/23510

DOI: 10.1103/PhysRevE.90.032915

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