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Virial Identities and Energy–Momentum Relation for Solitary Waves of Nonlinear Dirac Equations

Lobachevskii Journal of Mathematics, 2020
Solitary waves of nonlinear Dirac, Maxwell--Dirac and Klein--Gordon--Dirac equations are considered. We deduce some virial identities and check that the energy-momentum relation for solitary waves coincides with the Einstein energy-momentum relation for ...
T V Dudnikova
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Reaction of the nonlinear Dirac equation to a nonlinear Schrodinger equation with a correction term

Journal of Physics A: Mathematical and General, 1994
Summary: We examine the low-energy limit of the nonlinear Dirac equation (NLDE) in \(1+ 1\) dimensions with a Lorentz scalar self-interaction. Unlike the nonlinear Schrödinger equation (NLSE), which is integrable, the NLDE is known to exhibit rich dynamics of the soliton-soliton collision when the relative speed of the solitons is small.
Toyama, F. M., Hosono, Y., Ilyas, B., Nogami, Y.   +3 more
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The explicit solutions to the nonlinear Dirac equation and Dirac-Klein-Gordon equation

Ricerche di Matematica, 2007
It is well known that the Cauchy problem for the wave equation in one dimension can be easily solved. \textit{J.-P. Dias} and \textit{M. Figueira} [Ric. Mat. 35, 309--316 (1986; Zbl 0658.35076)] have shown, that the squared argument of a solution of the so called nonlinear Dirac equation \(\partial_tu + \alpha\partial_xu = i|u|^2u\), \(\alpha\) being a
Machihara, Shuji, Omoso, Takayuki
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ON SEMICLASSICAL GROUND STATES OF A NONLINEAR DIRAC EQUATION

Reviews in Mathematical Physics, 2012
This paper is concerned with existence and concentration phenomena of semiclassical solutions of the following nonlinear Dirac equation [Formula: see text] for x ∈ ℝ3 where pj ∈ (2, 3) are subcritical. Under some conditions, we show that there are two families of semiclassical solutions, for ℏ > 0 small, with the least energy, one concentrating on ...
Ding, Yanheng, Liu, Xiaoying
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Quantization for a nonlinear Dirac equation

Proceedings of the American Mathematical Society, 2016
We study solutions of certain nonlinear Dirac-type equations on Riemann spin surfaces. We first improve an energy identity theorem for a sequence of such solutions with uniformly bounded energy in the case of a fixed domain. Then, we prove the corresponding energy identity in the case that the equations have constant coefficients and the domains ...
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B�cklund transformations as nonlinear Dirac equations

Letters in Mathematical Physics, 1977
It is pointed out that the Backlund transformations for a physically interesting class of nonlinear partial differential equations can be interpreted as generalisations of the Cauchy Riemann equations or as nonlinear Dirac equations. The generalisations are inhomogenisations of the Cauchy Riemann equations (or their hyperbolic analogue), whose ...
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New nonlinear Dirac equation

Russian Physics Journal, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Linear and nonlinear Dirac equation

Foundations of Physics, 1993
Using the usual matrix representation of Clifford algebra of spacetime, quantities independent of the choice of a representation in the Dirac theory are examined, relativistic invariance of the theory is discussed, and a nonlinear equation is proposed.
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NONLINEAR DIRAC EQUATIONS WITH APPLICATIONS TO NEUTRINO OSCILLATIONS

International Journal of Modern Physics A, 2009
We first review a method to generate nonlinear Dirac equations. The method demands the nonlinear extensions preserve several physical properties like locality, Hermiticity, Poincaré invariance and separability. The last constraint results in nonlinear extensions of non-polynomial type.
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On semiclassical states of a nonlinear Dirac equation

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2013
We study the semiclassical limit of the least energy solutions to the nonlinear Dirac equation for x ∈ ℝ3. We prove that the equation has least energy solutions for all ħ > 0 small, and, in addition, that the solutions converge in a certain sense to the least energy solution of the associated limit problem as ħ → 0.
Y. H. Ding, C. Lee, B. Ruf
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