Transparent potential for the one-dimensional Dirac equation

1992 ◽  
Vol 45 (7) ◽  
pp. 5258-5261 ◽  
Author(s):  
Y. Nogami ◽  
F. M. Toyama
Keyword(s):  
Dirac Equation ◽  
One Dimensional ◽  
Transparent Potential ◽  
The One

scholarly journals Intertwining technique for the one-dimensional stationary Dirac equation

2003 ◽  
Vol 305 (2) ◽  
pp. 151-189 ◽  
Author(s):  
L.M. Nieto ◽  
A.A. Pecheritsin ◽  
Boris F. Samsonov
Keyword(s):  
Dirac Equation ◽  
One Dimensional ◽  
The One ◽  
Stationary Dirac Equation

Unilateral Global Bifurcation from Infinity in Nonlinearizable One-Dimensional Dirac Problems

2021 ◽  
Vol 31 (01) ◽  
pp. 2150005
Author(s):  
Ziyatkhan S. Aliyev ◽  
Nazim A. Neymatov ◽  
Humay Sh. Rzayeva
Keyword(s):  
Dirac Equation ◽  
Eigenvalue Problems ◽  
Global Bifurcation ◽  
Nontrivial Solutions ◽  
One Dimensional ◽  
Bifurcation From Infinity ◽  
The One ◽  
Nodal Properties

In this paper, we study the unilateral global bifurcation from infinity in nonlinearizable eigenvalue problems for the one-dimensional Dirac equation. We show the existence of two families of unbounded continua of the set of nontrivial solutions emanating from asymptotically bifurcation intervals and having the usual nodal properties near these intervals.

Inversion of transmission for the one‐dimensional Dirac equation

1992 ◽  
Vol 60 (6) ◽  
pp. 537-539
Author(s):  
G. J. Clerk ◽  
A. J. Davies
Keyword(s):  
Dirac Equation ◽  
One Dimensional ◽  
The One

Scattering operator for the one-dimensional Dirac equation with power nonlinearity

2016 ◽  
Vol 13 (04) ◽  
pp. 821-832
Author(s):  
Nakao Hayashi ◽  
Hironobu Sasaki
Keyword(s):  
Dirac Equation ◽  
Sobolev Space ◽  
Weighted Sobolev Space ◽  
Scattering Operator ◽  
One Dimensional ◽  
Power Nonlinearity ◽  
Nonlinear Dirac Equation ◽  
The One

We consider the nonlinear Dirac equation with a power nonlinearity [Formula: see text] where [Formula: see text], [Formula: see text]. We prove the existence of the scattering operator in the neighborhood of the origin of the weighted Sobolev space [Formula: see text], where [Formula: see text].

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