scholarly journals Group analysis and variational principle for nonlinear (3+1) schrodinger equation

2010 ◽  
Vol 7 (1) ◽  
pp. 115-122
Author(s):  
Eman Salem A. Alaidarous
Keyword(s):  
Variational Principle ◽  
Schrödinger Equation ◽  
Conservation Laws ◽  
Lie Groups ◽  
Schrodinger Equation ◽  
Group Analysis ◽  
Lie Symmetry ◽  
Functional Integral ◽  
Symmetry Groups ◽  
Conserved Currents

The generators of the admitted variational Lie symmetry groups are derived and conservation laws for the conserved currents are obtained via Noether's theorem. Moreover, the consistency of a functional integral are derived for the nonlinear Schrödinger equation. In addition to this analysis functional integral are studied using Lie groups.

Optical soliton group invariant solutions by optimal system of Lie subalgebra with conservation laws of the resonance nonlinear Schrödinger equation

2020 ◽  
Vol 34 (35) ◽  
pp. 2050402 ◽  
Author(s):  
Vinita ◽  
Santanu Saha Ray
Keyword(s):  
Schrödinger Equation ◽  
Conservation Laws ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Lie Symmetry ◽  
Nonlinear Schrodinger Equation ◽  
Invariant Solutions ◽  
Plasma Dynamic ◽  
One Dimensional ◽  
Nonlinear Schrödinger

In this article, the resonance nonlinear Schrödinger equation is studied, which elucidates the propagation of one-dimensional long magnetoacoustic waves in a cold plasma, dynamic of solitons and Madelung fluids in various nonlinear systems. The Lie symmetry analysis is used to achieve the invariant solution and similarity reduction of the resonance nonlinear Schrödinger equation. The infinitesimal generators, symmetry groups, commutator table and adjoint table have been obtained by the aid of invariance criterion of Lie symmetry. Also, one-dimensional system of subalgebra is constructed with the help of adjoint representation of a Lie group on its Lie algebra. By one-dimensional optimal subalgebra, the main equations are reduced to ordinary differential equations and their invariant solutions are provided. The general conservation theorem has been used to establish a set of non-local and non-trivial conservation laws.

scholarly journals Lie symmetry analysis, conservation laws and analytical solutions for chiral nonlinear Schrödinger equation in (2 + 1)-dimensions

2020 ◽  
Vol 25 (3) ◽  
Author(s):  
Jin-Jin Mao ◽  
Shou-Fu Tian ◽  
Tian-Tian Zhang ◽  
Xing-Jie Yan
Keyword(s):  
Schrödinger Equation ◽  
Conservation Laws ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Lie Symmetry ◽  
Nonlinear Schrodinger Equation ◽  
Symmetry Analysis ◽  
Optimal System ◽  
Lie Symmetry Analysis ◽  
Nonlinear Schrödinger

In this work, we consider the chiral nonlinear Schrödinger equation in (2 + 1)-dimensions, which describes the envelope of amplitude in many physical media. We employ the Lie symmetry analysis method to study the vector field and the optimal system of the equation. The similarity reductions are analyzed by considering the optimal system. Furthermore, we find the power series solution of the equation with convergence analysis. Based on a new conservation law, we construct the conservation laws of the equation by using the resulting symmetries. 

A fractal modification of Chen–Lee–Liu equation and its fractal variational principle

2021 ◽  
pp. 2150214
Author(s):  
Ji-Huan He ◽  
Chun-Hui He ◽  
Tareq Saeed
Keyword(s):  
Variational Principle ◽  
Solitary Wave ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Inverse Method ◽  
Ultrashort Pulses

The Chen–Lee–Liu equation is a modified Schrödinger equation to describe a solitary wave of ultrashort pulses in optics, which lead to a discontinuous time, so a fractal modification is suggested and a fractal variational principle is established by the semi-inverse method.

scholarly journals Lie symmetry analysis of the effects of urban infrastructures on residential property values

PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0255233
Author(s):  
Chien-Wen Lin ◽  
Jen-Cheng Wang ◽  
Bo-Yan Zhong ◽  
Joe-Air Jiang ◽  
Ya-Fen Wu ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Mean Squared Error ◽  
House Prices ◽  
Property Values ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Residential Property ◽  
Lie Symmetry Analysis ◽  
Residential Property Values

Due to the complexity of socio-economic-related issues, people thought of housing market as a chaotic nucleus situated at the intersection of neighboring sciences. It has been known that the dependence of house features on the residential property value can be estimated employing the well-established hedonic regression analysis method in teams of location characteristic, neighborhood characteristic and structure characteristic. However, to further assess the roles of urban infrastructures in housing markets, we proposed a new kind of volatility measure for house prices utilizing the Lie symmetry analysis of quantum theory based on Schrödinger equation, mainly focusing on the effects of transportation systems and public parks on residential property values. Based on the municipal open government data regularly collected for four cities, including Boston, Milwaukee, Taipei and Tokyo, and all spatial sampling sites were featured by United States Geological Survey (USGS) National Map, transportation and park were modelled as perturbations to the quantum states generated by the feature space in response to the environmental amenities with different spatial extents. In an attempt to ascertain the intrinsic impact of the location-dependent price information obtained, the similarity functions associated with the Schrödinger equation were considered to facilitate revealing the city amenities capitalizing into house prices. By examining the spatial spillover phenomena of house prices in the four cities investigated, it was found that the mass transit systems and the public green lands possessed the infinitesimal generators of Lie point symmetries Y2 and Y5, respectively. Compared statistically with the common performance criteria, including mean absolute error (MAE), mean squared error (MSE) and, root mean squared error (RMSE) obtained by hedonic pricing model, the Lie symmetry analysis of the Schrödinger equation approach developed herein was successfully carried out. The invariant-theoretical characterizations of economics-related phenomena are consonant with the observed residential property values of the cities internationally, ultimately leading to develop a new perspective in the global financial architecture.

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