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- W4285050470 abstract "We study the spectral stability of the nonlinear Dirac operator in dimension $1+1$, restricting our attention to nonlinearities of the form $f(langlepsi,beta psirangle_{mathbb{C}^2}) beta$. We obtain bounds on eigenvalues for the linearized operator around standing wave solutions of the form $e^{-iomega t} phi_0$. For the case of power nonlinearities $f(s)= s |s|^{p-1}$, $p>0$, we obtain a range of frequencies $omega$ such that the linearized operator has no unstable eigenvalues on the axes of the complex plane. As a crucial part of the proofs, we obtain a detailed description of the spectra of the self-adjoint blocks in the linearized operator. In particular, we show that the condition $langlephi_0,beta phi_0rangle_{mathbb{C}^2} > 0$ characterizes groundstates analogously to the Schrodinger case." @default.
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- W4285050470 date "2023-03-05" @default.
- W4285050470 modified "2023-09-29" @default.
- W4285050470 title "Results on the Spectral Stability of Standing Wave Solutions of the Soler Model in 1-D" @default.
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- W4285050470 doi "https://doi.org/10.1007/s00220-023-04646-4" @default.
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