scholarly journals Exact Solutions for a Modified Schrödinger Equation

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 908 ◽  
Author(s):  
Yassine Benia ◽  
Marianna Ruggieri ◽  
Andrea Scapellato
Keyword(s):  
Nonlinear Optics ◽  
Schrödinger Equation ◽  
Exact Solutions ◽  
Systematic Study ◽  
Schrodinger Equation ◽  
Higher Order ◽  
Lie Symmetry ◽  
Biological Science ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis

The aim of this paper was to propose a systematic study of a ( 1 + 1 ) -dimensional higher order nonlinear Schrödinger equation, arising in two different contexts regarding the biological science and the nonlinear optics. We performed a Lie symmetry analysis and here present exact solutions of the equation.

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.

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. 

Lie symmetry analysis, abundant exact solutions and dynamics of multisolitons to the $$(2+1)$$-dimensional KP-BBM equation

Pramana ◽  
2021 ◽  
Vol 95 (1) ◽  
Author(s):  
Sachin Kumar ◽  
Dharmendra Kumar ◽  
Harsha Kharbanda
Keyword(s):  
Exact Solutions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Bbm Equation

scholarly journals Lie symmetry analysis, optimal systems and exact solutions to the fifth-order KdV types of equations

2010 ◽  
Vol 368 (2) ◽  
pp. 551-558 ◽  
Author(s):  
Hanze Liu ◽  
Jibin Li ◽  
Lei Liu
Keyword(s):  
Exact Solutions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Fifth Order

New exact solutions of Bratu Gelfand model in two dimensions using Lie symmetry analysis

2020 ◽  
Vol 65 ◽  
pp. 198-206 ◽  
Author(s):  
Mohamed R. Ali ◽  
Wen-Xiu Ma
Keyword(s):  
Exact Solutions ◽  
Lie Symmetry ◽  
Two Dimensions ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
New Exact Solutions
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