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Nonlinear Dirac Equations [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2009
We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance.
Wei Khim Ng, Rajesh R. Parwani
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Nonlinear Dirac equations on Riemann surfaces [PDF]

Annals of Global Analysis and Geometry, 2007
We develop analytical methods for nonlinear Dirac equations. Examples of such equations include Dirac-harmonic maps with curvature term and the equations describing the generalized Weierstrass representation of surfaces in three-manifolds. We provide the
Chen, Qun, Jost, Juergen, Wang, Guofang
core   +6 more sources

Nonlinear Dirac Equations, Monotonicity Formulas and Liouville Theorems. [PDF]

Commun Math Phys, 2019
Abstract We study the qualitative behavior of nonlinear Dirac equations arising in quantum field theory on complete Riemannian manifolds. In particular, we derive monotonicity formulas and Liouville theorems for solutions of these equations. Finally, we extend our analysis to Dirac-harmonic maps with curvature term.
Branding V.
europepmc   +8 more sources

Solitary waves in the Nonlinear Dirac Equation [PDF]

, 2017
In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three ...
A Alvarez, A Alvarez, A Berthier, A Comech, A Comech, A Contreras, A Degasperis, A Galindo, A Guo, A Jensen, A Regensburger, A Ruschhaupt, A Soffer, AF Rañada, Andreas Fring, B Feng, B Peng, B Ramachandhran, B Thaller, B Waerden van der, B Wit De, B. V. Fedosov, C Hamner, C Jones, C Kharif, C Qu, C Sulem, Carl M Bender, CE Rüter, CJ Pethick, CM Bender, CM Bender, CM Bender, D Darby, D Pelinovsky, D Stuart, DD Ivanenko, DE Pelinovsky, DE Pelinovsky, DJ Gross, E Hairer, EH Lieb, F Cooper, F Merle, F Merle, FG Mertens, G Berkolaiko, G Berkolaiko, G Herring, GH Derrick, GJ Conduit, GL Alfimov, H Berestycki, H Huh, H Kestelman, H Sakaguchi, HM Quiney, IL Bogolubsky, IM Sigal, IV Barashenkov, J Alexander, J Bjorken, J Cuevas-Maraver, J Cuevas-Maraver, J Cuevas-Maraver, J Dalibard, J Evans, J Evans, J Evans, J Evans, J Radić, J Schindler, J Schindler, J Xu, JP Boyd, JR Dormand, KF Mak, KG Makris, KG Makris, L Gross, L Hadzievski, L Visscher, L Vázquez, LF Shampine, LH Haddad, LH Haddad, LH Haddad, LJ LeBlanc, LN Trefethen, LP Pitaevskii, M Chugunova, M Escobedo, M Grillakis, M Johansson, M Merkl, M Soler, M Soler, M Wakano, Maria J. Esteban, MJ Ablowitz, MJ Ablowitz, MJ Ablowitz, MJ Esteban, MJ Esteban, MJ Esteban, MJ Esteban, N Bournaveas, N Boussaïd, N Boussaïd, N Boussaïd, N Boussaïd, NG Vakhitov, O Fialko, O Peleg, P Blanchard, P Dirac, P Mathieu, PG Kevrekidis, PG Kevrekidis, R Carretero-González, R Finkelstein, RA Vicencio, RL Pego, RS MacKay, S Aubry, S Coleman, S Cuccagna, S Klaiman, S Machihara, S Machihara, S Rota Nodari, S Rota Nodari, S Selberg, S Shao, SY Lee, T Candy, T Cazenave, T Cazenave, T Dauxois, T Kapitula, T Kawakami, TO Wehling, TRO Melvin, TX Tran, V Achilleos, V Achilleos, V Georgiev, W Heisenberg, W Ng, W Pauli, WA Strauss, WE Thirring, WH Press, XQ Xu, Y Xu, YJ Lin, YS Kivshar, YV Kartashov   +157 more
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Nonlinear conformal-degree preserving Dirac equations

International Journal of Theoretical Physics, 2013
Nonlinear Dirac equations in D+1 space-time are obtained by variation of the spinor action whose Lagrangian components have the same conformal degree and the coupling parameter of the self-interaction term is dimensionless. In 1+1 dimension, we show that
Alhaidari, A. D.
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Nonlinear Dirac equation for graphene [PDF]

Keldysh Institute Preprints, 2016
The possibility of introducing a nonlinear correction to the Dirac equation for graphene in order to adequately describe collective electronic phenomena is considered. In contrast to the other papers on this topic the interaction term includes the sum of the spinor components’ squares instead of their difference.
Andrey Andreevich Gladkikh, Georgii Gennadyevich Malinetskii   +1 more
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Constraining Non-linear Dirac Equations with Neutrino Oscillations [PDF]

EPJ Web of Conferences, 2019
Considering the phenomenological studies of non-linear quantum models, we use an axiomatic approach to modify the Dirac Lagrangian. We apply constraints such as Hermiticity, locality, universality, etc to obtain various generic modified energy dispersion
Cheung James Asikin, Ng Wei Khim
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Parametrically driven nonlinear Dirac equation with arbitrary nonlinearity [PDF]

Journal of Physics A: Mathematical and Theoretical, 2020
The damped and parametrically driven nonlinear Dirac equation with arbitrary nonlinearity parameter $ $ is analyzed, when the external force is periodic in space and given by $f(x) =r\cos(K x)$, both numerically and in a variational approximation using five collective coordinates (time dependent shape parameters of the wave function).
Fred Cooper, Avinash Khare, Niurka R Quintero, Bernardo Sánchez-Rey, Franz G Mertens, Avadh Saxena   +5 more
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Analytical method of optical wave behavior studying in nonlinear medium with periodically arranged conducting nanofilms [PDF]

Известия высших учебных заведений: Прикладная нелинейная динамика, 2023
The purpose of this work is to build the analytical model of the behavior of a harmonic wave in a nonlinear optical medium with periodically arranged nanofilms. Methods.
Volkova, Svetlana Anatolena, Vytovtov, Konstantin Анатольевич, Barabanova, Elizaveta Aleksandrovna, Hahomov, Sergey Anatolevich, Kovalenko, Dmitry Leonidovich, Ivanov, Mihail Germanovich   +5 more
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Nonlinear A-Dirac Equations [PDF]

Advances in Applied Clifford Algebras, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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