Results 171 to 180 of about 2,989 (204)

An integrating factor for nonlinear Dirac equations

Computer Physics Communications, 2010
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Francisco de la Hoz, Fernando Vadillo
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On nonlinear Dirac equations

Journal of Mathematical Physics, 2019
This paper is concerned with the multiplicity of solutions for the nonlinear Dirac equation −i∑k=13αk∂ku+(V(x)+a)βu+ωu=Fu(x,u), where V (x) is a potential function and F(x, u) is a nonlinear function modeling various types of interactions. Under suitable assumptions on V (x) and F(x, u), we prove the existence of infinitely many geometrically distinct ...
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On the integrability of nonlinear Dirac equations

Journal of Mathematical Physics, 1984
The integrability of nonlinear Dirac equations is discussed applying recent results in soliton theory. Using the Lie point transformation groups of the nonlinear Dirac equations we reduce these partial differential equations to systems of ordinary differential equations and study whether these systems are integrable.
Steeb, W.-H., Oevel, W., Strampp, W.
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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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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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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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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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New nonlinear Dirac equation

Russian Physics Journal, 2012
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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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