New exact solutions of coupled (2+1)-dimensional nonlinear systems of Schrödinger equations

2011 ◽  
Vol 51 ◽  
pp. 110 ◽  
Author(s):  
F. Khani ◽  
M. T. Darvishi ◽  
Abbas Farmany ◽  
L. Kavitha
Keyword(s):  
Nonlinear Systems ◽  
Exact Solutions ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
New Exact Solutions

scholarly journals N-Fold Darboux Transformation for the Classical Three-Component Nonlinear Schrödinger Equations and Its Exact Solutions

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 733
Author(s):  
Yu-Shan Bai ◽  
Peng-Xiang Su ◽  
Wen-Xiu Ma
Keyword(s):  
Exact Solutions ◽  
Gauge Transformation ◽  
Darboux Transformation ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Lax Pairs ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
The Given

In this paper, by using the gauge transformation and the Lax pairs, the N-fold Darboux transformation (DT) of the classical three-component nonlinear Schrödinger (NLS) equations is given. In addition, by taking seed solutions and using the DT, exact solutions for the given NLS equations are constructed.

scholarly journals EXACT SOLUTIONS OF EFFECTIVE-MASS SCHRÖDINGER EQUATIONS

2002 ◽  
Vol 17 (37) ◽  
pp. 2453-2465 ◽  
Author(s):  
BÜLENT GÖNÜL ◽  
OKAN ÖZER ◽  
BEŞIRE GÖNÜL ◽  
FATMA ÜZGÜN
Keyword(s):  
Exact Solutions ◽  
Quantum Wells ◽  
Effective Mass ◽  
Wave Functions ◽  
Schrodinger Equations ◽  
Band Offset ◽  
Schrödinger Equations ◽  
Exact Solvability ◽  
Equivalent Systems ◽  
General Method

We outline a general method for obtaining exact solutions of Schrödinger equations with a position-dependent effective mass and compare the results with those obtained within the frame of supersymmetric quantum theory. We observe that the distinct effective mass Hamiltonians proposed in the literature in fact describe exactly equivalent systems having identical spectra and wave functions as far as exact solvability is concerned. This observation clarifies the Hamiltonian dependence of the band-offset ratio for quantum wells.

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