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Approximate Solution to Nonlinear Dynamics of a Piezoelectric Energy Harvesting Device Subject to Mechanical Impact and Winkler-Pasternak Foundation. [PDF]

Materials (Basel)
Marinca V, Herisanu N, Marinca B.
europepmc   +1 more source

Structure of Dirac matrices and invariants for nonlinear Dirac equations

Structure of Dirac matrices and invariants for nonlinear Dirac equations
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Bifurcation solutions for a nonlinear Dirac equation

Applied Mathematics Letters, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yuanyang Yu
exaly   +3 more sources

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 ...
Sihong Shao, Huazhong Tang
exaly   +3 more sources

Solitary Waves in the Nonlinear Dirac Equation [PDF]

Understanding Complex Systems, 2018
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 spatial dimensions and the equations they satisfy.
Jesus Cuevas-Maraver, Nabile Boussaid, Andrew Comech   +2 more
exaly   +4 more sources

The explicit solutions to the nonlinear Dirac equation and Dirac-Klein-Gordon equation

Ricerche Di Matematica, 2007
It is well known that the Cauchy problem for the wave equation in one dimension can be easily solved. \textit{J.-P. Dias} and \textit{M. Figueira} [Ric. Mat. 35, 309--316 (1986; Zbl 0658.35076)] have shown, that the squared argument of a solution of the so called nonlinear Dirac equation \(\partial_tu + \alpha\partial_xu = i|u|^2u\), \(\alpha\) being a
Shuji Machihara
exaly   +3 more sources