Results 221 to 230 of about 471,361 (266)

Infinitely many localized semiclassical states for critical nonlinear Dirac equations

Nonlinearity, 2021
In this paper, we are concerned with semiclassical states to the nonlinear Dirac equation with Sobolev critical exponent −iϵα⋅∇u+aβu+V(x)u=|u|q−2u+|u|uinR3 , where u:R3→C4 , 2 < q < 3, ϵ > 0 is a small parameter, a > 0 is a constant, α = (α 1, α 2, α 3),
Shaowei Chen, Tian-Xiang Gou
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Soliton solutions of nonlinear Dirac equations

Journal of Mathematical Physics, 1979
Dirac equations with fourth order self-couplings are investigated in one time and three space dimensions. Both stringlike and ball-like soliton solutions carrying nontopological quantum numbers are shown to exist, depending on the symmetries taken into account.
K. Takahashi
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Periodic waves of nonlinear Dirac equations

Nonlinear Analysis: Theory, Methods & Applications, 2014
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Yanheng Ding, Xiaoying Liu
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Linearized Crank-Nicholson scheme for nonlinear Dirac equations

Journal of Computational Physics, 1992
The author presents a finite-difference algorithm (a linearized Crank-Nicolson scheme) to solve nonlinear Dirac systems. The lack of iterations in this algorithm, without decreasing its accuracy, is the principal difference with the Crank-Nicolson scheme. Applications are demonstrated and discussed.
A. Alvarez
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New nonlinear Dirac equation

Russian Physics Journal, 2012
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B�cklund transformations as nonlinear Dirac equations

Letters in Mathematical Physics, 1977
It is pointed out that the Backlund transformations for a physically interesting class of nonlinear partial differential equations can be interpreted as generalisations of the Cauchy Riemann equations or as nonlinear Dirac equations. The generalisations are inhomogenisations of the Cauchy Riemann equations (or their hyperbolic analogue), whose ...
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Linear and nonlinear Dirac equation

Foundations of Physics, 1993
Using the usual matrix representation of Clifford algebra of spacetime, quantities independent of the choice of a representation in the Dirac theory are examined, relativistic invariance of the theory is discussed, and a nonlinear equation is proposed.
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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
Machihara, Shuji, Omoso, Takayuki
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Nonrelativistic limit and nonexistence of stationary solutions of nonlinear Dirac equations

Journal of Differential Equations, 2023
Xiaojing Dong, Yanheng Ding, Qi Guo
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Ground states solutions for nonlinear Dirac equations

Ricerche di Matematica, 2022
This paper concerns the ground state solutions for the partial differential equations known as the Dirac equations. Under suitable assumptions on the nonlinearity, we show the existence of nontrivial and ground state solutions.
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