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.

ON A QUANTUM VERSION OF CONSERVATION LAWS FOR DERIVATIVE NONLINEAR SCHRÖDINGER EQUATION

1988 ◽  
Vol 03 (09) ◽  
pp. 893-900
Author(s):  
SHIBANI SEN ◽  
A. ROY CHOWDHURY
Keyword(s):  
Schrödinger Equation ◽  
Conservation Laws ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Quantum Mechanical ◽  
Conserved Quantities ◽  
Nonlinear Schrödinger ◽  
Quantum Version ◽  
Derivative Nonlinear Schrödinger Equation

We have derived the quantum mechanical versions of infinite number of conservation laws associated with Derivative Nonlinear Schrödinger equation with the help of a methodology used in string theory. The renormalised version of the conserved quantities are obtained with explicit forms of the counter terms.

scholarly journals Exact Solutions of the Generalized Nonlinear Schrodinger Equation

2021 ◽  
pp. 18-25
Author(s):  
Gaukhar Shaikhova ◽  
Arailym Syzdykova ◽  
Samgar Daulet
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Physical Problems ◽  
Different Types ◽  
Generalized Nonlinear Schrödinger Equation

In this work, the generalized nonlinear Schrodinger equation is investigated. Exact solutions are derived by the sinecosine method. This method is used to obtain the exact solutions for different types of nonlinear partial differential equations. Graphs of obtained solutions are presented. The obtained solutions are found to be important for the explanation of some practical physical problems.

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