scholarly journals Constructing solvable models of vector non-linear Schrödinger equation with balanced loss and gain via non-unitary transformation

2021 ◽  
pp. 127361
Author(s):  
Pijush K. Ghosh
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Unitary Transformation ◽  
Solvable Models ◽  
Non Linear

The dissipative property of a cubic non-linear Schrödinger equation

2015 ◽  
Vol 79 (2) ◽  
pp. 346-374 ◽  
Author(s):  
P I Naumkin
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Dissipative Property ◽  
Non Linear

A meshfree approach for analysis and computational modeling of non-linear Schrödinger equation

2020 ◽  
Vol 39 (2) ◽  
Author(s):  
Ram Jiwari ◽  
Sanjay Kumar ◽  
R. C. Mittal ◽  
Jan Awrejcewicz
Keyword(s):  
Schrödinger Equation ◽  
Computational Modeling ◽  
Schrodinger Equation ◽  
Non Linear

The interaction representation in the quantum theory of fields

1950 ◽  
Vol 201 (1065) ◽  
pp. 284-296 ◽  
Keyword(s):  
Quantum Theory ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Unitary Transformation ◽  
Present Theory ◽  
Point Of View ◽  
Field Equations ◽  
Generalized Schrödinger Equation ◽  
Invariant Interaction ◽  
Theory Of Fields

The interaction representation has recently been introduced into the quantum theory of fields by Tomonaga and Schwinger. Applications of the theory to interacting meson-photon fields have led to apparent difficulties in determining invariant interaction Hamiltonians. Another troublesome feature is the necessity of verifying the integrability conditions of the so-called generalized Schrödinger equation. In the present paper the theory of the interaction representation is presented from a different point of view. It is shown that if two field operators with the same transformation character satisfy two different field equations, there is a unique unitary transformation connecting the field variables on any space-like surface given such a correspondence on one given space-like surface. A differential equation for determining this unique unitary transformation is found which is the analogue of Tomonaga’s generalized Schrödinger equation. This gives directly and simply an invariant interaction Hamiltonian and renders unnecessary the explicit verification of the integrability of the Schrödinger equation, since this is known to have a unique solution. To illustrate the simplification introduced by the present theory, the interaction Hamiltonian for the interacting scalar meson-photon fields is calculated. The result is the same as that obtained by Kanesawa & Tomonaga, but it is obtained by a straightforward calculation without the need to add terms to make the Hamiltonian an invariant.

scholarly journals Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable Derivative

2020 ◽  
Vol 8 ◽  
Author(s):  
Hemen Dutta ◽  
Hatıra Günerhan ◽  
Karmina K. Ali ◽  
Resat Yilmazer
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Conformable Derivative ◽  
Non Linear ◽  
Exact Soliton Solutions

scholarly journals Soliton emission in the forced non-linear Schrödinger equation

1986 ◽  
Vol 4 (3-4) ◽  
pp. 545-553 ◽  
Author(s):  
O. Larroche ◽  
M. Casanova ◽  
D. Pesme ◽  
M. N. Bussac
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Reasonable Agreement ◽  
Critical Density ◽  
Plasma Waves ◽  
Resonant Absorption ◽  
Direct Numerical Simulations ◽  
Absorption Of Light ◽  
Non Linear ◽  
Soliton Generation

The plasma waves generated by resonant absorption of light in the vicinity of the critical density of laser-produced plasmas, are modelled by a non-linear Schrödinger equation with additional terms accounting for the presence of a source and the inhomogeneity of the medium.We use an average lagrangian method to describe the behaviour of the solutions of this equation in the range of parameters where periodic soliton generation occurs. An iterating scheme describing the successive emission of solitons yields values for this range of parameters which are in reasonable agreement with those found from direct numerical simulations of the non-linear Schrödinger equation.

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