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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
doaj   +8 more sources

The cubic nonlinear Dirac equation [PDF]

Journées équations aux dérivées partielles, 2012
We present some results obtained in collaboration with prof. Piero D'Ancona concerning global existence for the 3D cubic non linear massless Dirac equation with a potential for small initial data in $H^1$ with slight additional assumptions.
Cacciafesta, Federico
core   +2 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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Numerical methods for nonlinear Dirac equation [PDF]

Journal of Computational Physics, 2013
This paper presents a review of the current state-of-the-art of numerical methods for nonlinear Dirac (NLD) equation. Several methods are extendedly proposed for the (1+1)-dimensional NLD equation with the scalar and vector self-interaction and analyzed ...
Shao, Sihong, Tang, Huazhong, Xu, Jian
core   +3 more sources

Periodic solutions for nonlinear Dirac equation with superquadratic nonlinearity

Electronic Journal of Differential Equations, 2016
This article concerns the periodic solutions for a nonlinear Dirac equation. Under suitable assumptions on the nonlinearity, we show the existence of nontrivial and ground state solutions.
Jian Zhang, Qiming Zhang, Xianhua Tang, Wen Zhang   +3 more
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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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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
openaire   +4 more sources

Caccioppoli-type inequalities for Dirac operators

Journal of Inequalities and Applications, 2022
In this paper, we establish the Caccioppoli estimates for the nonlinear differential equation − D ‾ ( | D v | p − 2 D v ) = λ | v | p − 2 v , 1 < p < ∞ , $$ - \overline{D}\bigl( \vert Dv \vert ^{p-2}Dv\bigr) = \lambda \vert v \vert ^{p-2}v, \quad 1< p ...
Ardak Kashkynbayev, Gulaiym Oralsyn
doaj   +1 more source

Nonlinear Vibration of a Beam Resting on a Nonlinear Viscoelastic Foundation Traversed by a Moving Mass: A Homotopy Analysis

Engineering Transactions, 2022
In this study, the dynamic response of an Euler-Bernoulli beam resting on the nonlinear viscoelastic foundation under the action of a moving mass by considering the stretching effect of the beam’s neutral axis is investigated.
Mehdi POURSEIFI, Mojtaba Mahmoudi MONFARED   +1 more
doaj   +1 more source

On spectral stability of solitary waves of nonlinear Dirac equation on a line [PDF]

, 2012
We study the spectral stability of solitary wave solutions to the nonlinear Dirac equation in one dimension. We focus on the Dirac equation with cubic nonlinearity, known as the Soler model in (1+1) dimensions and also as the massive Gross-Neveu model ...
A. Comech, Buslaev, Buslaev, Cazenave, Cuccagna, Cuccagna, Derrick, G. Berkolaiko, Grillakis, Grillakis, Gross, Gross, Lee, Shatah, Shatah, Shatah, Soffer, Soffer, Soler, Vakhitov, Weinstein, Weinstein, Zakharov   +22 more
core   +3 more sources