Dynamical symmetries of rotationally invariant, three‐dimensional, Schrödinger equations

1980 ◽  
Vol 21 (4) ◽  
pp. 807-817 ◽  
Author(s):  
D. R. Truax
Keyword(s):  
Three Dimensional ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Dynamical Symmetries ◽  
Rotationally Invariant

LOD-MS for Gross-Pitaevskii Equation in Bose-Einstein Condensates

2013 ◽  
Vol 14 (1) ◽  
pp. 219-241 ◽  
Author(s):  
Linghua Kong ◽  
Jialin Hong ◽  
Jingjing Zhang
Keyword(s):  
Energy Conservation ◽  
Computational Cost ◽  
Three Dimensional ◽  
Schrodinger Equations ◽  
Pitaevskii Equation ◽  
Schrödinger Equations ◽  
One Dimensional ◽  
Exactly Solvable ◽  
Bose Einstein ◽  
Energy Conservation Law

AbstractThe local one-dimensional multisymplectic scheme (LOD-MS) is developed for the three-dimensional (3D) Gross-Pitaevskii (GP) equation in Bose-Einstein condensates. The idea is originated from the advantages of multisymplectic integrators and from the cheap computational cost of the local one-dimensional (LOD) method. The 3D GP equation is split into three linear LOD Schrödinger equations and an exactly solvable nonlinear Hamiltonian ODE. The three linear LOD Schrödinger equations are multisymplectic which can be approximated by multisymplectic integrator (MI). The conservative properties of the proposed scheme are investigated. It is mass-preserving. Surprisingly, the scheme preserves the discrete local energy conservation laws and global energy conservation law if the wave function is variable separable. This is impossible for conventional MIs in nonlinear Hamiltonian context. The numerical results show that the LOD-MS can simulate the original problems very well. They are consistent with the numerical analysis.

scholarly journals Analytic solutions of the chiral nonlinear schrödinger equations investigated by an efficient approach

2019 ◽  
Vol 7 (2) ◽  
pp. 94
Author(s):  
K. M. Abdul Al Woadud ◽  
Dipankar Kumar ◽  
Md. Jahirul Islam ◽  
Md. Imrul Kayes ◽  
Atish Kumar Joardar
Keyword(s):  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Analytic Solutions ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
New Exact Solutions ◽  
Nonlinear Schrodinger Equations ◽  
Kudryashov Method

This paper studies the chiral nonlinear Schrödinger equations, describing a central role in the developments of quantum me-chanics, particularly in the field of quantum Hall effect, where chiral excitations are known to appear. More precisely, in this paper, we acquired new exact solutions of the chiral nonlinear (1+1) and (1+2)-dimensional Schrödinger equations by using the modified Kudraysov method. As outcomes, some of the new exact traveling wave solutions for the equations above is formally produced. All solutions are plotted in the view of three-dimensional (3D) and two-dimensional (2D) line shape through the MATLAB software for investigating the real significance of the studied equations. The periodic type of solitons is generated by employing modified Kudryashov method which is different from other studied methods. 

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