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Structure of Dirac matrices and invariants for nonlinear Dirac equations
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Bifurcation solutions for a nonlinear Dirac equation
Applied Mathematics Letters, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yuanyang Yu
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The explicit solutions to the nonlinear Dirac equation and Dirac-Klein-Gordon equation
Ricerche Di Matematica, 2007It 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
Shuji Machihara
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An integrating factor for nonlinear Dirac equations
Computer Physics Communications, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Francisco de la Hoz, Fernando Vadillo
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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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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, 1984The 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, 1994Summary: 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. +3 more
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ON SEMICLASSICAL GROUND STATES OF A NONLINEAR DIRAC EQUATION
Reviews in Mathematical Physics, 2012This 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, 2016We 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, 1977It 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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