Results 11 to 20 of about 76,709 (184)
Solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity [PDF]
Physical Review E, 2010 15 pages, 7 ...
Cooper, Fred +3 more
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The One-Dimensional Dirac Equation With Concentrated Nonlinearity [PDF]
SIAM Journal on Mathematical Analysis, 2017 The purpose of this paper is to study the one-dimensional Dirac equation with a new kind of singular operator. By the self-adjointness of the extension of this operator, the authors are able to study a wide range of similar well-posed equations, which are parametrized through a singular boundary condition.
CACCIAPUOTI, CLAUDIO +3 more
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Nonlinear Dirac equation solitary waves in external fields [PDF]
Physical Review E, 2012 We consider the nonlinear Dirac equations (NLDE's) in 1+1 dimension with scalar-scalar self interaction $\frac{g^2}{ +1} ({\bPsi} )^{ +1}$ in the presence of various external electromagnetic fields. Starting from the exact solutions for the unforced problem we study the behavior of solitary wave solutions to the NLDE in the presence of a wide ...
Mertens, Franz G. +4 more
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Waves in Honeycomb Structures [PDF]
, 2012 We review recent work of the authors on the non-relativistic Schr\"odinger equation with a honeycomb lattice potential, $V$. In particular, we summarize results on (i) the existence of Dirac points, conical singularities in dispersion surfaces of $H_V ...
Fefferman, Charles L. +1 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 in the way of the accuracy and the time reversibility as well as the conservation of the discrete ...
Xu, Jian, Shao, Sihong, Tang, Huazhong
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Gradient catastrophe of nonlinear photonic valley-Hall edge pulses
Physical Review Research, 2021 We derive nonlinear wave equations describing the propagation of slowly varying wave packets formed by topological valley-Hall edge states. We show that edge pulses break up even in the absence of spatial dispersion due to nonlinear self-steepening. Self-
Daria A. Smirnova +4 more
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Vibrations of a geometrically nonlinear viscoelastic shallow shell with concentrated masses [PDF]
E3S Web of Conferences, 2021 Shell structures are widely used in various fields of technology and construction. Often, they play the role of a bearing surface with assemblies, overlays, and aggregates installed on them.
Vatin Nikolai +2 more
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Pseudo-Exponential-Type Solutions of Wave Equations Depending on Several Variables [PDF]
, 2015 Using matrix identities, we construct explicit pseudo-exponential-type solutions of linear Dirac, Loewner and Schr\"odinger equations depending on two variables and of nonlinear wave equations depending on three ...
Fritzsche, Bernd +3 more
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Born-infeld electrodynamics: Clifford number and spinor representations
International Journal of Mathematics and Mathematical Sciences, 2002 The Clifford number formalism for Maxwell equations is considered. The Clifford imaginary unit for space-time is introduced as coordinate independent form of fully antisymmetric fourth-rank tensor.
Alexander A. Chernitskii
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A remark on nonlinear Dirac equations [PDF]
Proceedings of the American Mathematical Society, 2010 For an n n -dimensional spin manifold M M with a fixed spin structure and a spinor bundle Σ M \Sigma M , we prove an ϵ \epsilon -regularity theorem for weak solutions to the nonlinear Dirac equation \[ ∂̸ ψ = H
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