Results 21 to 30 of about 82,530 (235)
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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Compact Implicit Integration Factor Method for the Nonlinear Dirac Equation
Discrete Dynamics in Nature and Society, 2017 A high-order accuracy numerical method is proposed to solve the (1+1)-dimensional nonlinear Dirac equation in this work. We construct the compact finite difference scheme for the spatial discretization and obtain a nonlinear ordinary differential system.
Jing-Jing Zhang +2 more
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Global bifurcation for nonlinear Dirac problems
Electronic Journal of Qualitative Theory of Differential Equations, 2016 In this paper we consider the nonlinear eigenvalue problems for the one-dimensional Dirac equation. To exploit oscillatory properties of the components of the eigenvector-functions of linear one-dimensional Dirac system an appropriate family of sets is ...
Ziyatkhan Aliyev, Humay Rzayeva
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On the GBDT version of the B\"acklund-Darboux transformation and its applications to the linear and nonlinear equations and Weyl theory [PDF]
, 2009 A general theorem on the GBDT version of the B\"acklund-Darboux transformation for systems rationally depending on the spectral parameter is treated and its applications to nonlinear equations are given.
Sakhnovich, Alexander
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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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Speed-of-light pulses in the massless nonlinear Dirac equation with a potential [PDF]
, 2017 We consider the massless nonlinear Dirac (NLD) equation in $1+1$ dimension with scalar-scalar self-interaction $\frac{g^2}{2} (\bar{\Psi} \Psi)^2$ in the presence of three external electromagnetic potentials $V(x)$, a potential barrier, a constant ...
Bishop, A. R. +4 more
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Solutions of nonlinear Dirac equations
Journal of Differential Equations, 2006 Existence and multiplicity results for stationary solutions of the Dirac equation \(-i\partial _{t}\psi =ic\hslash \sum_{k=1}^{3}a_{k}\partial _{k}\psi -mc^{2}\beta \psi +\nabla _{\psi }G(x,\psi )\) are established via variational method. The associated Lagrangian functional is strongly indefinite and the Palais-Smale (PS) condition is not satisfied ...
Bartsch, Thomas, Ding, Yanheng
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A SHOCK LAYER ARISING AS THE SOURCE TERM COLLAPSES IN THE P(X)-LAPLACIAN EQUATION
Проблемы анализа, 2020 We study the Cauchy–Dirichlet problem for the p(x)-Laplacian equation with a regular finite nonlinear minor term. The minor term depends on a small parameter ε > 0 and, as ε → 0, converges weakly* to the expression incorporating the Dirac delta function,
S. N. Antontsev +2 more
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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 key analytical steps, i.e., small energy regularity and removable singularity theorems and energy ...
Chen, Qun, Jost, Jürgen, Wang, Guofang
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Gauge Invariance of Nonlinear Klein-Gordon
Positron, 2013 We have discussed the gauge invariance of nonlinear Klein-Gordon equation which describes the interaction of electromagnetic initially proposed by Hermann Weyl. The construction of nonlinear Klein-Gordon itself is formulated by two classical conservation
T. B. Prayitno
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