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• W1995703657 abstract "We consider the nonlinear Dirac equation in 1+1 dimension with scalar-scalar self interaction $ frac{g^2}{kappa+1} ({bar Psi} Psi)^{kappa+1}$ and with mass $m$. Using the exact analytic form for rest frame solitary waves of the form $Psi(x,t) = psi(x) e^{-i omega t}$ for arbitrary $ kappa$, we discuss the validity of various approaches to understanding stability that were successful for the nonlinear Schrodinger equation. In particular we study the validity of a version of Derrick's theorem, 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 4th-order operator splitting integration method. For different ranges of $kappa$ we map out the stability regimes in $omega$. 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 $t_c$, it takes for the instability to set in, is an exponentially increasing function of $omega$ and $t_c$ decreases monotonically with increasing $kappa$." @default.
• W1995703657 created "2016-06-24" @default.
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• W1995703657 date "2014-09-17" @default.
• W1995703657 modified "2023-10-17" @default.
• W1995703657 title "Stability of solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity" @default.
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• W1995703657 doi "https://doi.org/10.1103/physreve.90.032915" @default.
• W1995703657 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/25314512" @default.
• W1995703657 hasPublicationYear "2014" @default.
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