scholarly journals On PT Symmetry Systems: Invariance, Conservation Laws, and Reductions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
P. Masemola ◽  
A. H. Kara
Keyword(s):  
Schrödinger Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Schrodinger Equation ◽  
Lie Symmetries ◽  
Pt Symmetry ◽  
Noether Symmetries ◽  
Cubic Schrödinger Equation ◽  
The Relationship

An analysis of a PT symmetric coupler with “gain in one waveguide and loss in another” is made; a transformation in the PT system and some assumptions results in a scalar cubic Schrödinger equation. We investigate the relationship between the conservation laws and Lie symmetries and investigate a Lagrangian, corresponding Noether symmetries, conserved vectors, and exact solutions via “double reductions.”

On the invariances, conservation laws, and conserved quantities of the damped–driven nonlinear Schrödinger equation

2012 ◽  
Vol 90 (2) ◽  
pp. 199-206 ◽  
Author(s):  
Anjan Biswas ◽  
P. Masemola ◽  
R. Morris ◽  
A.H. Kara
Keyword(s):  
Partial Differential Equations ◽  
Schrödinger Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Dispersive Media ◽  
Conserved Quantities ◽  
Nonlinear Schrödinger

We study the invariance, exact solutions, conservation laws, and double reductions of the nonlinear Schrödinger equation with damping and driving terms. The underlying equation is used to model a variety of resonant phenomena in nonlinear dispersive media, inter alia. For the purpose of our analysis, the complex equation is construed as a system of two real partial differential equations.

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