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• W2218378425 abstract "In this study we consider we consider a prototypical example of a <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$mathcal {P}$</tex-math> </inline-formula> <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$mathcal {T}$</tex-math></inline-formula> -symmetric Dirac model. We discuss the underlying linear limit of the model and identify the threshold of the <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$mathcal {P}$ </tex-math></inline-formula> <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$mathcal {T}$</tex-math></inline-formula> -phase transition in an analytical form. We then focus on the examination of the nonlinear model. We consider the continuation in the <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$mathcal {P}$</tex-math></inline-formula> <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$mathcal {T}$</tex-math> </inline-formula> -symmetric model of the solutions of the corresponding Hamiltonian model and find that the solutions can be continued robustly as stable ones all the way up to the <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$mathcal {P}$</tex-math> </inline-formula> <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$mathcal {T}$</tex-math></inline-formula> -transition threshold. In the latter, they degenerate into linear waves. We also examine the dynamics of the model. Given the stability of the waveforms in the <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$mathcal {P}$</tex-math></inline-formula> <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX> $mathcal {T}$</tex-math></inline-formula> -exact phase, we consider them as initial conditions for parameters outside of that phase. We find that both oscillatory dynamics and exponential growth may arise, depending on the size of the corresponding “quench”. The former can be characterized by an interesting form of bifrequency solutions that have been predicted on the basis of the SU <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$(1,1)$</tex-math></inline-formula> symmetry. Finally, we explore some special, analytically tractable, but not <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$mathcal {P}$</tex-math> </inline-formula> <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$mathcal {T}$</tex-math></inline-formula> -symmetric solutions in the massless limit of the model." @default.
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• W2218378425 date "2016-09-01" @default.
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• W2218378425 title "Solitary Waves of a <inline-formula> <tex-math notation=LaTeX>$mathcal {P}$</tex-math> </inline-formula><inline-formula> <tex-math notation=LaTeX>$mathcal {T}$</tex-math> </inline-formula>-Symmetric Nonlinear Dirac Equation" @default.
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• W2218378425 doi "https://doi.org/10.1109/jstqe.2015.2485607" @default.
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