Conservation Laws for the Derivative Nonlinear Schrödinger Equation with Non-vanishing Boundary Conditions

2005 ◽  
Vol 22 (4) ◽  
pp. 830-832 ◽  
Author(s):  
Chen Xiang-Jun ◽  
Hou Li-Jie ◽  
Lam Wa Kun
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Conservation Laws ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Derivative Nonlinear Schrödinger Equation

Some generalized coupled nonlinear Schrödinger equations and conservation laws

2017 ◽  
Vol 31 (32) ◽  
pp. 1750299 ◽  
Author(s):  
Wei Liu ◽  
Xianguo Geng ◽  
Bo Xue
Keyword(s):  
Schrödinger Equation ◽  
Conservation Laws ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Matrix Problem ◽  
Nonlinear Schrödinger ◽  
Curvature Equation ◽  
Zero Curvature ◽  
Derivative Nonlinear Schrödinger Equation

Based on zero-curvature equation, a series of new four-component nonlinear Schrödinger-type equations related to a [Formula: see text] matrix problem are proposed by using the polynomial expansion of the spectral parameter. As two special reductions, a generalized coupled nonlinear Schrödinger equation and a generalized coupled derivative nonlinear Schrödinger equation are obtained. And then, the infinite conservation laws for each of these four-component nonlinear Schrödinger-type equations are constructed with the aid of the Riccati-type 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.

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