scholarly journals Non-local \mathcal{PT} -symmetric potentials in the one-dimensional Dirac equation

2008 ◽  
Vol 41 (50) ◽  
pp. 505305 ◽  
Author(s):  
Francesco Cannata ◽  
Alberto Ventura
Keyword(s):  
Dirac Equation ◽  
One Dimensional ◽  
Non Local ◽  
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.

scholarly journals Uniqueness of one-dimensional Néel wall profiles

2016 ◽  
Vol 472 (2187) ◽  
pp. 20150762 ◽  
Author(s):  
Cyrill B. Muratov ◽  
Xiaodong Yan
Keyword(s):  
Domain Wall ◽  
Energy Functional ◽  
Wall Structure ◽  
One Dimensional ◽  
Uniform Estimates ◽  
Limiting Behaviour ◽  
Non Local ◽  
The One ◽  
Wall Profile ◽  
Domain Wall Structure

We study the domain wall structure in thin uniaxial ferromagnetic films in the presence of an in-plane applied external field in the direction normal to the easy axis. Using the reduced one-dimensional thin-film micromagnetic model, we analyse the critical points of the obtained non-local variational problem. We prove that the minimizer of the one-dimensional energy functional in the form of the Néel wall is the unique (up to translations) critical point of the energy among all monotone profiles with the same limiting behaviour at infinity. Thus, we establish uniqueness of the one-dimensional monotone Néel wall profile in the considered setting. We also obtain some uniform estimates for general one-dimensional domain wall profiles.

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