Results 1 to 10 of about 471,361 (266)
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, Monotonicity Formulas and Liouville Theorems. [PDF]
Commun Math Phys, 2019 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.
Branding V.
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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
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Low-regularity integrators for nonlinear Dirac equations [PDF]
Mathematics of Computation, 2019 In this work, we consider the numerical integration of the nonlinear Dirac equation and the Dirac–Poisson system (NDEs) under rough initial data. We propose an ultra low-regularity integrator (ULI) for solving the NDEs which enables optimal first-order ...
Katharina Schratz +2 more
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Weakly localized states for nonlinear Dirac equations [PDF]
Calculus of Variations and Partial Differential Equations, 2018 We prove the existence of infinitely many non square-integrable stationary solutions for a family of massless Dirac equations in 2D. They appear as effective equations in two dimensional honeycomb structures.
William Borrelli
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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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Strongly localized semiclassical states for nonlinear Dirac equations [PDF]
Discrete and Continuous Dynamical Systems. Series A, 2020 We study semiclassical states of the nonlinear Dirac equation \[ -i\hbar\partial_t\psi = ic\hbar\sum_{k=1}^3\alpha_k\partial_k\psi - mc^2\beta \psi - M(x)\psi + f(|\psi|)\psi,\quad t\in\mathbb{R},\ x\in\mathbb{R}^3, \] where $V$ is a bounded continuous ...
T. Bartsch, T. Xu
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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 +5 more
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Rigorous derivation of nonlinear Dirac equations for wave propagation in honeycomb structures [PDF]
, 2016 We consider a nonlinear Schroedinger equation in two spatial dimensions subject to a periodic honeycomb lattice potential. Using a multi-scale expansion together with rigorous error estimates, we derive an effective model of nonlinear Dirac type.
J. Arbunich, Christof Sparber
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Potential well and multiplicity of solutions for nonlinear Dirac equations
Communications on Pure and Applied Analysis, 2020 In this paper we consider the semi-classical solutions of a massive Dirac equations in presence of a critical growth nonlinearity \begin{document}$ -i\hbar \sum\limits_{k = 1}^{3}\alpha_k\partial_k w+a\beta w+V(x)w = f(|w|)w.
Yu Chen, Yanheng Ding, T. Xu
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