scholarly journals Time-Compact Scheme for the One-Dimensional Dirac Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Jun-Jie Cao ◽  
Xiang-Gui Li ◽  
Jing-Liang Qiu ◽  
Jing-Jing Zhang
Keyword(s):  
Dirac Equation ◽  
Fourth Order ◽  
Compact Scheme ◽  
Order Accuracy ◽  
Spectral Order ◽  
Unconditionally Stable ◽  
Numerical Examples ◽  
One Dimensional ◽  
The One ◽  
Discrete Charge

Based on the Lie-algebra, a new time-compact scheme is proposed to solve the one-dimensional Dirac equation. This time-compact scheme is proved to satisfy the conservation of discrete charge and is unconditionally stable. The time-compact scheme is of fourth-order accuracy in time and spectral order accuracy in space. Numerical examples are given to test our results.

Compact splitting symplectic scheme for the fourth-order dispersive Schrödinger equation with Cubic-Quintic nonlinear term

2019 ◽  
Vol 10 (02) ◽  
pp. 1950007 ◽  
Author(s):  
Lang-Yang Huang ◽  
Zhi-Feng Weng ◽  
Chao-Ying Lin
Keyword(s):  
Schrödinger Equation ◽  
Fourth Order ◽  
Schrodinger Equation ◽  
Nonlinear Term ◽  
Order Accuracy ◽  
Numerical Examples ◽  
Splitting Technique ◽  
Symplectic Scheme ◽  
Theoretical Results ◽  
Discrete Charge

Combining symplectic algorithm, splitting technique and compact method, a compact splitting symplectic scheme is proposed to solve the fourth-order dispersive Schrödinger equation with cubic-quintic nonlinear term. The scheme has fourth-order accuracy in space and second-order accuracy in time. The discrete charge conservation law and stability of the scheme are analyzed. Numerical examples are given to confirm the theoretical results.

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.

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